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Due to the intermittent and unstable nature of PV systems, maximum power point tracking (MPPT) of PV systems is necessary in practice. At the same time, PV cells are also shaded by objects such as trees and houses in the environment causing local shadows, so the Lévy flight particle swarm optimisation (LFPSO) is proposed in this paper. The random walk process of Lévy flight is added to the particle swarm optimisation (PSO) to increase the diversity of the search, which can avoid falling into local optimal solutions. The experimental simulation results show that the algorithm proposed in this paper can still accurately track the global maximum power in the case of partial shading, which well avoids falling into the local maximum power. The performance is much higher than the traditional maximum power point tracking algorithm, which improves the efficiency of the PV system. [ABSTRACT FROM AUTHOR]

This paper is concerned with the optimal portfolio problem for a company that can invest in two risky assets, where a novel Lévy-process-driven model is constructed to describe the dynamics of the wealth process by using a constant elasticity of variance model and a jump-diffusion process. A delicately designed value function is proposed under the mean–variance criterion to reflect the optimal portfolio for the stochastic volatility model. By using the verification theorem, the desired optimal portfolio strategy is proposed by the solution to certain Hamilton–Jacobi–Bellman equations. Furthermore, the corresponding expressions are achieved by using the stochastic analysis theory. Finally, a numerical simulation example is provided to verify the effectiveness of the proposed optimal portfolio strategy. [ABSTRACT FROM AUTHOR]

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The paper considers dimensional synthesis of a path generator four-bar linkage by applying the modified Differential Evolution (DE) algorithm. During the search of the space, the DE algorithm may skip the right solution and lead to premature convergence. If the step is reduced, the search space is reduced as well, so that convergence becomes slower. Search efficiency may be achieved by including Lévy Flight in the DE algorithm. Namely, when the DE algorithm identifies the space of best solution, then a Levý Flight step is used for local search in that region, which significantly increases the exploitation capability and allows obtaining a very efficient solution of the optimization problem. The algorithm was tested with three examples of dimensional synthesis of a path generator four-bar linkage. The proposed algorithm can be very efficiently applied to solving very complex optimization problems. [ABSTRACT FROM AUTHOR]

This paper studies the Cramér–Lundberg asymptotics of the ruin probability for a model in which the reserve level process is described by a spectrally-positive light-tailed Markov additive process. By applying a change-of-measure technique in combination with elements from Wiener-Hopf theory, the exact asymptotics of the ruin probability are expressed in terms of the model primitives. In addition a simulation algorithm of generalized Siegmund type is presented, under which the returned estimate of the ruin probability has bounded relative error. Numerical experiments show that, compared to direct estimation, this algorithm greatly reduces the number of runs required to achieve an estimate with a given accuracy. The experiments also reveal that our asymptotic results provide a good approximation of the ruin probability even for relatively small initial surplus levels. [ABSTRACT FROM AUTHOR]

This paper endeavours to directly establish the observability inequality of backward stochastic heat equations involving a Lévy process for measurable sets. As an immediate application, we attain the approximate controllability of forward stochastic heat equations featuring a Lévy process. Subsequently, we embark upon the formulation of a nuanced optimization problem, encompassing both the determination of an optimal actuator location and its associated minimum norm control. This formulation is elegantly cast as a two-person zero-sum game problem. We then proceed to articulate a set of conditions–both sufficient and necessary–required for optimizing the solution through the prism of a Nash equilibrium. At last, we prove that the relaxed optimal solution is an optimal actuator location for the classical problem. [ABSTRACT FROM AUTHOR]

In the process of milling titanium alloy, workpiece surface roughness is mainly affected by cutting parameters, tool angle, tool shape and system vibration. There is a complex highly nonlinear relationship among these factors, which makes it impossible to build an accurate mathematical model. Therefore, an effective surface roughness prediction method is of great significance to improve machining efficiency and reduce machining cost. In this paper, taking flank milling Ti6Al4 V alloy as an example, a surface roughness prediction framework (SRPF) based on CLBAS-BP algorithm is proposed. Chaotic Lorentz system and Lévy flight strategy are used to optimize BAS algorithm, which can improve local search ability, solution precision and convergence speed. CLBAS-BP algorithm has higher prediction accuracy than other algorithms, and can predict workpiece surface roughness with various cutting parameters. This study provides the technique foundation for improving the high-precision manufacturing of products. [ABSTRACT FROM AUTHOR]

In this paper, we develop the James–Stein improved method for the estimation problem of a nonparametric periodic function observed with Lévy noises in continuous time. An adaptive model selection procedure based on the weighted improved least squares estimates is constructed. The improvement effect for nonparametric models is studied. It turns out that in non-asymptotic setting the accuracy improvement for nonparametric models is more important than for parametric ones. Moreover, sharp oracle inequalities for the robust risks have been shown and the adaptive efficiency property for the proposed procedures has been established. The numerical simulations are given. [ABSTRACT FROM AUTHOR]

In the present paper, we investigate the optimal investment strategies for an insurer with the liquid constraint. The insurer's surplus is modeled by a Lévy process. The insurer can invest in N risky assets and a risk-free asset. However, in reality, the insurer needs to keep partial amount of his wealth as liquid reserves to meet with the management, which is called as the liquid constraint. We assume that the liquid reserve is a proportion of the insurer's wealth. Using the martingale approach, we derive the explicit optimal investment strategies for both CARA and quadratic utilities. [ABSTRACT FROM AUTHOR]

This paper discusses Parisian ruin problem under drawdown with capital injection when the underlying source of randomness of the surplus is modeled by a general Lévy insurance risk process. Capital injection is provided at the first instance the surplus drops below the drawdown level that is a pre-specified function of its current maximum. The capital is continuously injected to keep the surplus above the drawdown level until either it goes above its current maximum or a Parisian type ruin occurs, which is announced at the first time the surplus process has undergone an excursion below its current maximum for an independent exponential period of time consecutively since the most recent drawdown time. Some distributional identities concerning this excursion are presented. Firstly, we give the Parisian ruin probability and the joint Laplace transform (possibly killed at the first passage time above a fixed level for the surplus process) of the ruin time, the surplus position at ruin, and the total capital injection at ruin. Secondly, we obtain the q-potential measure of the surplus process killed at Parisian ruin. Finally, we give the expected present value of the total discounted capitals injected up to the Parisian ruin time. The results are derived using recent developments in fluctuation and excursion theory of spectrally negative Lévy process and are presented semi-explicitly in terms of the scale function of the Lévy process. Some numerical examples are given to facilitate the analysis of the impact of initial surplus and frequency of observation periods to the ruin probability and to the expected total discounted capital injection. [ABSTRACT FROM AUTHOR]

This paper discusses the long-range dependence in the risk-neutral stock return process of the S&P 500 index option market. To observe the long-range dependence together with fat-tails, I define the parametric model of fractional Lévy process. Since the continuous time fractional Lévy process allows arbitrage, I use discrete time option pricing model based on the fractional Lévy process. By model calibration, we can capture the long-range dependence in the S&P 500 index option market. The paper finds that the long range dependence becomes stronger for the volatile market caused by the Lehman Brothers Collapse, comparing with other less volatility markets. [ABSTRACT FROM PUBLISHER]

In this paper, a risk model driven by spectrally negative Lévy processes is considered where dividends until a general draw-down time are paid under a constant barrier strategy. In this model, the moments of the sum of the discounted dividend payments until the general draw-down time are derived through the corresponding scale functions. The explicit expressions for the Laplace transform of the discounted dividends are also obtained. Moreover, numerical examples are given to illustrate the impacts of barrier levels and draw-down functions on the results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonstandard renewal multi-risk model where a company has n types of independent insurance contracts and each contract has some dependent claims and stochastic return. The price process of the investment portfolio is described as a geometric Lévy process. When the claim size distribution belongs to the class of , we can get some asymptotic formulae for the tail probability of n types contracts' discounted aggregate claims and ruin probabilities, holding uniformly for some finite horizons. [ABSTRACT FROM AUTHOR]

In this paper, we concentrate on the European option pricing problem in incomplete markets by taking Vasicek stochastic interest rate model into account and expanding it in accordance with a Lévy process named Variance Gamma (VG) process. In doing so, first, we prove the existence and uniqueness of the solution to the stochastic differential equation of this model. Then, by the means of the hedging and replicating techniques, pricing formulas for the bond and, in succession, for European options are established. Finally, from a numerical point of view, we will analyze the value of a bond based on our consideration model and also, we will study a European call option bond price. All these results are reported through the Monte-Carlo simulation method. [ABSTRACT FROM AUTHOR]

The paper tackles the stabilization of stochastic hybrid neural networks. Different from the existing work which the Brownian motion was used to stabilize neural networks for the stochastic stability, the stabilization is generalized by Lévy noise in this paper. To address the unobservable items in the hybrid neural networks, we introduce the Markov chain into the hybrid neural networks and divide the state space of Markov chain into two subsets for observable and unobservable items. Then, the sufficient conditions of stabilization and destabilization for the stochastic neural networks are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we present a sequential hypothesis test for the detection of the distribution of jump size in Lévy processes. Infinitesimal generators for the corresponding log-likelihood ratios are presented and analysed. Bounds for infinitesimal generators in terms of super-solutions and sub-solutions are computed. This is shown to be implementable in relation to various classification problems for a crude oil price data set. Machine and deep learning algorithms are implemented to extract a specific deterministic component from the data set, and the deterministic component is implemented to improve the Barndorff-Nielsen & Shephard model, a commonly used stochastic model for derivative and commodity market analysis. [ABSTRACT FROM AUTHOR]

The main task of this paper is to model the dependency and effects of the Lehman Brothers financial collapse event using a superposed and coupled Ornstein-Uhlenbeck type system of stochastic differential equations driven by a Lévy process. The development of these types of efficient models to correctly quantify and predict the sample paths of these kinds of time series is essential since it helps prevent losses or maximize profits in the field of financial modeling. The results obtained from this study suggest that the solutions of the stochastic models provide a good fit to the high frequency financial stock market data since it captures realistic dependence structures. In addition, the estimated model parameters are useful for making inferences and predicting these types of events. [ABSTRACT FROM AUTHOR]

This paper applies an algorithm for the convolution of compactly supported Legendre series (the CONLeg method) (cf. Hale and Townsend, An algorithm for the convolution of Legendre series. SIAM J. Sci. Comput., 2014, 36, A1207–A1220), to pricing European-type, early-exercise and discrete-monitored barrier options under a Lévy process. The paper employs Chebfun (cf. Trefethen et al., Chebfun Guide, 2014 (Pafnuty Publications: Oxford), Available online at: ) in computational finance and provides a quadrature-free approach by applying the Chebyshev series in financial modelling. A significant advantage of using the CONLeg method is to formulate option pricing and option Greek curves rather than individual prices/values. Moreover, the CONLeg method can yield high accuracy in option pricing when the risk-free smooth probability density function (PDF) is smooth/non-smooth. Finally, we show that our method can accurately price options deep in/out of the money and with very long/short maturities. Compared with existing techniques, the CONLeg method performs either favourably or comparably in numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we focused on computing the minimal relative entropy between the original probability and all of the equivalent martin gale measure for the Lévy process. For this purpose, the quasiMonte Carlo method is used. The probability with minimal relative entropy has many suitable properties. This probability has the minimal Kullback-Leibler distance to the original probability. Also, by using the minimal relative entropy the exponential utility indifference price can be found. In this paper, the Monte Carlo and quasi-Monte Carlo methods have been applied. In the quasi-Monte Carlo method, two types of widely used lowdiscrepancy sequences, Halton sequence and Sobol sequence, are used. These methods have been used for exponential Lévy process such as variance gamma and CGMY process. In these two processes, the minimal relative entropy has been computed by Monte Carlo and quasi-Monte Carlo, and compared their results. The results show that quasi-Monte Carlo with Sobol sequence performs better in terms of fast convergence and less error. Finally, this method by fitting the variance gamma model and parameters estimation for the model has been implemented for financial data and the corresponding minimal relative entropy has been computed. [ABSTRACT FROM AUTHOR]

In this paper, the asymptotic behavior of solutions for a nonlinear Marcus stochastic differential equation with multiplicative two-sided Lévy noise is studied. We plan to consider this equation as a random dynamical system. Thus, we have to interpret a Lévy noise as a two-sided metric dynamical system. For that, we have to introduce some fundamental properties of such a noise. So far most studies have only discussed two-sided Lévy processes which are defined by combining two-independent Lévy processes. In this paper, we use another definition of two-sided Lévy process by expanding the probability space. Having this metric dynamical system we will show that the Marcus stochastic differential equation with a particular drift coefficient and multiplicative noise generates a random dynamical system which has a random attractor. [ABSTRACT FROM AUTHOR]

In this paper, we unify two popular approaches for the definition of actuarial ruin with implementation delays, also known as Parisian ruin. Our new definition of ruin includes both deterministic delays and exponentially distributed delays: ruin is declared the first time an excursion in the red zone lasts longer than an implementation delay with a deterministic and a stochastic component. For this Parisian ruin with mixed delays, we identify the joint distribution of the time of ruin and the deficit at ruin, therefore providing generalizations of many results previously obtained, such as in Baurdoux et al. (2016) and Loeffen et al. (in press) for the case of an exponential delay and that of a deterministic delay, respectively. [ABSTRACT FROM AUTHOR]

On account of that the OU models based on Gaussian process cannot describe the characteristics of peak, bias and asymmetric thick tail in SHIBOR time series, this paper replaces the Gaussian process in OU model with Levy process which can be decomposed into positive and negative subordinate processes, constructs OU model based on positive and negative subordinate processes. Methods parameter estimation and stochastic simulation were carried out by making discrete the stochastic differential equations into stochastic difference equations. The result shows that non-Gaussian OU process based on positive and negative subordinate processes not only fits the time series but also has better economic interpretation. The innovation of our research is to build a model of Non-Gaussian OU process based on positive and negative subordinate processes with less stochastic terms, and it provides an efficient tool for forecasting SHIBOR time series. [ABSTRACT FROM AUTHOR]

The threshold dividend strategy, under which dividends are paid only when the insurer's surplus exceeds a pre-determined threshold, has received considerable attention in risk theory. However, in practice, it seems rather unlikely that an insurer will immediately pull back the dividend payments as soon as its surplus level drops below the dividend threshold. Hence, in this paper, we propose a refracted Lévy risk model with delayed dividend pullbacks triggered by a certain Poissonian observation scheme. Leveraging the extensive literature on fluctuation identities for spectrally negative Lévy processes, we obtain explicit expressions for two-sided exit identities of the proposed insurance risk process. Also, penalties are incorporated into the analysis of dividend payouts as a mechanism to penalize for the volatility of the dividend policy and account for an investor's typical preference for more stable cash flows. An explicit expression for the expected (discounted) dividend payouts net of penalties is derived. The criterion for the optimal threshold level that maximizes the expected dividend payouts is also discussed. Finally, several numerical examples are considered to assess the impact of dividend delays on ruin-related quantities. We numerically show that dividend strategies with more steady dividend payouts can be preferred (over the well-known threshold dividend strategy) when penalty fee become too onerous. [ABSTRACT FROM AUTHOR]

The classical Cramér–Lundberg risk process is commonly used to model the surplus of an insurer; it characterizes the claim arrival process and the claim size random variable Y through a compound Poisson process, along with a constant rate of premium income. When E (Y 2) < ∞ , the process can be approximated by a diffusion process, but that requirement eliminates many heavy-tailed claim models, such as the Pareto (α , θ) with α ≤ 2. In this paper, we generalize the well known diffusion approximation by assuming that Y lies in the domain of attraction of an α-stable random variable, for 0 < α ≤ 2. Then, we construct a sequence of classical Cramér–Lundberg risk processes and show that the sequence converges to an α-stable Lévy motion in the Skorokhod J 1 -topology. We prove this convergence by proving the pointwise convergence of the corresponding Laplace exponents of our processes, which to our knowledge, is a new result. To apply this convergence result, we show the convergence of a sequence of Gerber–Shiu distributions of exponential Parisian ruin, and we show the convergence of a sequence of payoff functions for barrier dividend strategies. Both of these applications provide new proofs of the stated limits. [ABSTRACT FROM AUTHOR]

Solving optimal stopping problems by backward induction in high dimensions is often very complex since the computation of conditional expectations is required. Typically, such computations are based on regression, a method that suffers from the curse of dimensionality. Therefore, the objective of this paper is to establish dimension reduction schemes for large-scale asset price models and to solve related optimal stopping problems (e.g., Bermudan option pricing) in the reduced setting, where regression is feasible. The proposed algorithm is based on an error measure between linear stochastic differential equations. We establish optimality conditions for this error measure with respect to the reduced system coefficients and propose a particular method that satisfies these conditions up to a small deviation. We illustrate the benefit of our approach in several numerical experiments, in which Bermudan option prices are determined. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a martingale representation theorem in the progressive enlargement G by a random time τ of the filtration F L generated by a Lévy process. The assumptions on the random time are that F L is immersed in G and that τ avoids F L stopping times. We also study the multiplicity of a progressively enlarged filtration. [ABSTRACT FROM AUTHOR]

This paper is devoted to study the well-known Razumikhin-type theorem for a class of stochastic functional differential equations with Lévy noise and Markov switching. In comparison to the standard Gaussian noise, Lévy noise and Markov switching make the analysis more difficult owing to the discontinuity of its sample paths. In this paper, we attempt to overcome this difficulty. By using the Razumikhin method and Lyapunov functions, we obtain several Razumikhin-type theorems to prove the pth moment exponential stability of the suggested system. Based on these results,we further discuss the pth moment exponential stability of stochastic delay differential equations with Lévy noise and Markov switching. In particular, the results obtained in this paper improve and generalise some previous works given in the literature. Finally, an example is provided to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper shows how the distributions-based portfolio separation theorem – also known as the mutual fund theorem – for elliptical and stable distributions carries over from a static to a continuous-time model. Without invoking Itô stochastic calculus, only the definition of the Itô integral, we generalize and simplify an approach of Khanna and Kulldorff (http://link.springer.com/article/10.1007%2Fs007800050056Finance Stoch. 3 (1999), pp. 167–185). In addition to (re-) covering the classical cases, this paper also gives separation results for non-symmetric stable distributions underno shorting-conditions, including a new case ofone fundseparation without risk-free opportunity. Applicability of the skewed cases to insurance and banking is discussed, as well as limitations. [ABSTRACT FROM PUBLISHER]

This paper studies optimal investment and risk control strategies for an insurer who owns insider information. The insurance risk process is governed by a general jump diffusion process with random parameters and is correlated with the risky asset process in the financial market. We model the inside information by a general random variable related to the insurance risk process and the risky asset process. Under the criterion of expected utility maximization of the terminal wealth, we adopt white noise calculus and BSDE approach to analyze the problem for various utility functions. [ABSTRACT FROM AUTHOR]

We study the pathwise uniqueness of the solutions to one-dimensional stochastic differential equations driven by Brownian motions and Lévy processes with finite variation paths. The driving Lévy processes are not necessarily one-sided jump processes. In this paper, we obtain some non-Lipschitz conditions on the coefficients, under which the pathwise uniqueness of the solution to the equations is established. Some of our results can be applied to the equation with discontinuous coefficients. [ABSTRACT FROM AUTHOR]

This paper presents a constructive method to design control inputs that almost surely globally K ∞ -exponentially stabilise strict-feedback systems driven by Lévy processes, which consist of Wiener and compensated Poisson processes, at the origin. The control design is based on a recently developed Lyapunov-type theorem for the study of well-posedness and almost sure K ∞ -exponential stability of SDEs driven by Lévy processes, the backstepping method, and new Lyapunov functions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of Poissonian occupation times below level 0 of a spectrally negative Lévy process. In this case, occupation time is accumulated only when the process is observed to be negative at arrival epochs of an independent Poisson process. Our results extend some well known continuously observed quantities involving occupation times of spectrally negative Lévy processes. As an application, we establish a link between Poissonian occupation times and insurance risk models with Parisian implementation delays. [ABSTRACT FROM AUTHOR]

Maximising dividends is one classical stability criterion in actuarial risk theory. Motivated by the fact that dividends are paid periodically in real life, periodic dividend strategies were recently introduced (Albrecher et al. 2011). In this paper, we incorporate fixed transaction costs into the model and study the optimal periodic dividend strategy with fixed transaction costs for spectrally negative Lévy processes. The value function of a periodic (b u , b l) strategy is calculated by means of exiting identities and Itô's excusion when the surplus process is of unbounded variation. We show that a sufficient condition for optimality is that the Lévy measure admits a density which is completely monotonic. Under such assumptions, a periodic (b u , b l) strategy is confirmed to be optimal. Results are illustrated. [ABSTRACT FROM AUTHOR]

This paper is concerned with partial-information mixed optimal stochastic continuous–singular control problem for mean-field stochastic differential equation driven by Teugels martingales and an independent Brownian motion, where the Teugels martingales are a family of pairwise strongly orthonormal martingales associated with Lévy processes. The control variable has two components; the first being absolutely continuous, and the second singular. Partial-information necessary and sufficient conditions of optimal continuous–singular control for these mean-field models are investigated. As an illustration, this paper studies a partial-information linear quadratic control problem of mean-field type involving continuous–singular control. [ABSTRACT FROM AUTHOR]

In this paper, we consider the partial integro-differential equation arising when a stock follows a Poisson distributed jump process, for the pricing of Asian options. We make use of the meshless radial basis functions with differential quadrature for approximating the spatial derivatives and demonstrate that the algorithm performs effectively well as compared to the commonly employed finite difference approximations. We also employ Strang splitting with the exponential time integration technique to improve temporal efficiency. Throughout the numerical experiments covered in the paper, we show how the proposed scheme can be efficiently employed for the pricing of American style Asian options under both the Black–Scholes and the Merton jump-diffusion models. [ABSTRACT FROM PUBLISHER]

This paper investigates the ruin probabilities of a renewal risk model with stochastic investment returns and dependent claim sizes. The investment is described as a portfolio of one risk-free asset and one risky asset whose price process is an exponential Lévy process. The claim sizes are assumed to follow a two-sided linear process with independent and identically distributed step sizes. When the step-size distribution is heavy tailed, the paper establishes some uniform asymptotic formulas of ruin probabilities. [ABSTRACT FROM PUBLISHER]

The stability of nonlinear stochastic differential equations driven by time-changed Lévy process with impulsive effects is discussed in this paper. Some sufficient conditions are provided to guarantee the solutions to be stable in different senses. The stochastic perturbation is also investigated for some unstable time-changed differential equations with impulses. The efficiency of the proposed results is illustrated by some examples with numerical simulations. [ABSTRACT FROM AUTHOR]

We apply a new numerical method, the singular Fourier--Padé (SFP) method invented by Driscoll and Fornberg [Numer. Algorithms, 2001, 26, 77-92; The Gibbs Phenomenon in Various Representations and Applications, 2011], to price European-type options in Lévy and affine processes. The motivation behind this application is to reduce the inefficiency of current Fourier techniques when they are used to approximate piecewise continuous (non-smooth) probability density functions. When techniques such as fast Fourier transforms and Fourier series are applied to price and hedge options with nonsmooth probability density functions, they cause the Gibbs phenomenon; accordingly, the techniques converge slowly for density functions with jumps in value or derivatives. This seriously adversely affects the efficiency and accuracy of these techniques. In this paper, we derive pricing formulae and their option Greeks using the SFP method to resolve the Gibbs phenomenon and restore the global spectral convergence rate. Moreover, we show that our method requires a small number of terms to yield fast error convergence, and it is able to accurately price any European-type option deep in/out of the money and with very long/short maturities. Furthermore, we conduct an error-bound analysis of the SFP method in option pricing. This new method performs favourably in numerical experiments compared with existing techniques. [ABSTRACT FROM AUTHOR]

We focus on mean-variance hedging problem for models whose asset price follows an exponential additive process. Some representations of mean-variance hedging strategies for jump-type models have already been suggested, but none is suited to develop numerical methods of the values of strategies for any given time up to the maturity. In this paper, we aim to derive a new explicit closed-form representation, which enables us to develop an efficient numerical method using the fast Fourier transforms. Note that our representation is described in terms of Malliavin derivatives. In addition, we illustrate numerical results for exponential Lévy models. [ABSTRACT FROM AUTHOR]

In this paper, an insurer is allowed to make risk-free and risky investments, and the price process of the investment portfolio is described as an exponential Lévy process. We study the asymptotic tail behavior for a non-standard renewal risk model with dependence structures. The claim sizes are assumed to follow a one-sided linear process with independent and identically distributed step sizes, and the step sizes and inter-arrival times form a sequence of independent and identically distributed random pairs with a dependence structure. When the step-size distribution is heavy tailed, we obtain some uniform asymptotics for the finite-and infinite-time ruin probabilities. [ABSTRACT FROM AUTHOR]

In this paper we find the Laplace transforms of the weighted occupation times for a spectrally negative Lévy surplus process to spend below its running maximum up to the first exit times. The results are expressed in terms of generalized scale functions. For step weight functions, the Laplace transforms can be further expressed in terms of scale functions. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of parameter estimation for the Ornstein–Uhlenbeck processes { d X t = θ X t d t + d Y t d Y t = Y t d t + ε d L t d driven by Ornstein–Uhlenbeck processes with small fractional Lévy noises and Yt can be observed, based on discrete high frequency observations at regularly spaced time points { t k = k n , k = 1 , ... , n } on [ 0 , 1 ]. We obtain the consistency as well as the asymptotic behavior of the least squares estimator of the unknown parameter θ when ε → 0 and n → ∞ simultaneously. [ABSTRACT FROM AUTHOR]

In this paper, we analyse a one-dimensional disordered waveguide array in which the refractive indices of the waveguides are selected to be random numbers drawn from a Lévy-type distribution characterized by the exponentα. We study the effect of changing the exponentαon the transverse localization effect. It is shown that the quality of transverse localization is improved by decreasing the exponentα. Furthermore, we study this effect for several refractive index ranges. The design of disordered waveguide arrays in this way permits control of the degree of transverse localization. [ABSTRACT FROM PUBLISHER]

In this paper we propose the study of the problem of the guaranteed minimum withdraw benefit (or GMWB for short) rider pricing by the means of American option pricing in the Lévy setting with a new method. Using wavelet discretization we reduce the problem to a matrix linear complementary problem giving the value function in the log price domain. Our approach with wavelets seems to be helpful in allowing practitioners to decide in advance how accurate a result they want and decide on the way whether to refine the mesh or stop the iteration procedure. [ABSTRACT FROM AUTHOR]

In this paper, we employ the martingale and duality methods to study the optimal investment and proportional reinsurance problem for an insurer. The insurer's risk process is modeled by a Lévy process and the capital can be invested in a security market described by a geometric Lévy process. The objective of the insurer is to maximize the expected utility of her terminal wealth. We derive the expression for optimal investment-reinsurance strategies for various utility functions. Furthermore, an example is considered, and numerical simulations are presented to illustrate the effect of the parameters on the optimal strategies. [ABSTRACT FROM AUTHOR]

In the present paper, a new and simple approach is provided for proving rigorously that for general Lévy financial markets the minimal entropy martingale measure and the Esscher martingale measure coincide. The method consists in approximating the probability measure P by a sequence of Lévy preserving probability measures P n with exponential moments of all order. As a by-product, it turns out that the problem of finding the minimal entropy martingale measure for the Lévy market is equivalent to the corresponding problem but for a certain one-step financial market. The existence of the Esscher martingale measure (and hence the minimal entropy martingale measure) will be characterized by using moment generating functions of the Lévy process. [ABSTRACT FROM AUTHOR]

The beetle antennae search (BAS) algorithm is a new meta-heuristic algorithm which has been shown to be very useful in many applications. However, the algorithm itself still has some problems, such as low precision and easy to fall into local optimum when solving complex problems, and excessive dependence on parameter settings. In this paper, an algorithm called beetle antennae search algorithm based on Lévy flights and adaptive strategy (LABAS) is proposed to solve these problems. The algorithm turns the beetle into a population and updates the population with elite individuals' information to improve the convergence rate and stability. At the same time, Lévy flights and scaling factor are introduced to enhance the algorithm's exploration ability. After that, the adaptive step size strategy is used to solve the problem of difficult parameter setting. Finally, the generalized opposition-based learning is applied to the initial population and elite individuals, which makes the algorithm achieve a certain balance between global exploration and local exploitation. The LABAS algorithm is compared with 6 other heuristic algorithms on 10 benchmark functions. And the simulation results show that the LABAS algorithm is superior to the other six algorithms in terms of solution accuracy, convergence rate and robustness. [ABSTRACT FROM AUTHOR]

In this paper, we define and characterize cointegrated solutions of continuous-time linear state-space models driven by Lévy processes. Cointegrated solutions of such models are shown to be representable as a sum of a Lévy process and a stationary solution of a linear state-space model, analogous to the Granger representation for cointegrated VAR models. Moreover, we prove that the class of cointegrated multivariate Lévy-driven autoregressive moving-average (MCARMA) processes, the continuous-time analogues of the classical vector ARMA processes, is equivalent to the class of cointegrated solutions of continuous-time linear state-space models. Necessary conditions for MCARMA processes to be cointegrated are given as well extending the results of Comte [Discrete and continuous time cointegration, J. Econometrics 88 (1999), pp. 207–226] for MCAR processes. The conditions depend only on the autoregressive polynomial if we have a minimal model. Finally, we investigate cointegrated continuous-time linear state-space models observed on a discrete time-grid and calculate their linear innovations. Based on the representation of the linear innovations, we derive an error correction form. The error correction form uses an infinite linear filter in contrast to the finite linear filter for VAR models. Some sufficient identifiable criteria are also given. [ABSTRACT FROM AUTHOR]

In this paper, we develop an arbitrage-free multiple curve model through the specification of forward swap rates. Two sets of assets are chosen as fundamentals: OIS zero-coupon bonds and forward rate agreements. This is a very natural approach since, on the one hand, OIS bonds represent the class of risk-free discount bonds and, on the other hand, the mid and long maturity part of the interest rate term structure is bootstrapped from quotes of swap rates that can be represented by FRA rates and OIS bond prices in the multiple curve setting. We construct the rates via a backward induction along the tenor structure on the basis of the forward swap measures. Time-inhomogeneous Lévy processes are used as drivers of the dynamics. As an application, we derive an approximative Fourier-based valuation formula for swaptions. The model is implemented and calibrated by using generalized hyperbolic Lévy processes as drivers. [ABSTRACT FROM AUTHOR]

This paper investigates a financial market where stock returns depend on a hidden Gaussian mean reverting drift process. Information on the drift is obtained from returns and expert opinions in the form of noisy signals about the current state of the drift arriving at the jump times of a homogeneous Poisson process. Drift estimates are based on Kalman filter techniques and described by the conditional mean and covariance matrix of the drift given the observations. We study the filter asymptotics for increasing arrival intensity of expert opinions and prove that the conditional mean is a consistent drift estimator; it converges in the mean-square sense to the hidden drift. Thus, in the limit as the arrival intensity goes to infinity investors have full information about the drift. [ABSTRACT FROM AUTHOR]