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We provide a characterization of an optimal stopping time for a class of finite horizon time-inconsistent optimal stopping problems (OSPs) of mean-field type, adapted to the Brownian filtration, including those related to mean-field diffusion processes and recursive utility functions. Despite the time-inconsistency of the OSP, we show that it is optimal to stop when the value-process hits the reward process for the first time, as is the case for the standard time-consistent OSP. We solve the problem by approximating the corresponding value-process with a sequence of Snell envelopes of processes, for which a sequence of optimal stopping times is constituted of the hitting times of each of the reward processes by the associated value-process. Then, under mild assumptions, we show that this sequence of hitting times converges in probability to the hitting time for the mean-field OSP and that the limit is optimal., QC 20230821

In this paper, we study a class of reflected backward stochastic differential equations (BSDEs) of mean-field type, where the mean-field interaction in terms of the distribution of the Y-component of the solution enters in both the driver and the lower obstacle. We consider in details the case where the lower obstacle is a deterministic function of (Y, E[Y]) and discuss the more general dependence on the distribution of Y. Under mild Lipschitz and in-tegrability conditions on the coefficients, we obtain the well-posedness of such a class of equations. Under further monotonicity conditions, we show convergence of the standard penalization scheme to the solution of the equa-tion, which hence satisfies a minimality property. This class of equations is motivated by applications in pricing life insurance contracts with surrender options., QC 20230810

This article considers importance sampling for estimation of rare-event probabilities in a specific collection of Markovian jump processes used for, e.g., modeling of credit risk. Previous attempts at designing importance sampling algorithms have resulted in poor performance and the main contribution of the article is the design of efficient importance sampling algorithms using subsolutions. The dynamics of the jump processes cause the corresponding Hamilton-Jacobi equations to have an intricate state-dependence, which makes the design of efficient algorithms difficult. We provide theoretical results that quantify the performance of importance sampling algorithms in general and construct asymptotically optimal algorithms for some examples. The computational gain compared to standard Monte Carlo is illustrated by numerical examples., QC 20220408

We study a class of infinite horizon impulse control problems with execution delay when the dynamics of the system is described by a general stochastic process adapted to the Brownian filtration. The problem is solved by means of probabilistic tools relying on the notion of Snell envelope and infinite horizon reflected backward stochastic differential equations. This allows us to establish the existence of an optimal strategy over all admissible strategies., QC 20220325

We consider the life-cycle optimal portfolio choice problem faced by an agent receiving labor income and allocating her wealth to risky assets and a riskless bond subject to a borrowing constraint. In this paper, to reflect a realistic economic setting, we propose a model where the dynamics of the labor income has two main features. First, labor income adjusts slowly to financial market shocks, a feature already considered in Biffis et al. (2015). Second, the labor income gamma i of an agent i is benchmarked against the labor incomes of a population gamma(n) := (gamma(1),gamma(2), ...,gamma(n)) of n agents with comparable tasks and/or ranks. This last feature has not been considered yet in the literature and is faced taking the limit when n -> +infinity so that the problem falls into the family of optimal control of infinite-dimensional McKean-Vlasov Dynamics, which is a completely new and challenging research field. We study the problem in a simplified case where, adding a suitable new variable, we are able to find explicitly the solution of the associated HJB equation and find the optimal feedback controls. The techniques are a careful and nontrivial extension of the ones introduced in the previous papers of Biffis et al. (2015, 0000). (C) 2021 Elsevier B.V. All rights reserved., QC 20220524

We introduce a class of one-dimensional continuous reflected backward stochastic Volterra integral equations driven by Brownian motion, where the reflection keeps the solution above a given stochastic process (lower obstacle). We prove existence and uniqueness by a fixed point argument and derive a comparison result. Moreover, we show how the solution of our problem is related to a time-inconsistent optimal stopping problem and derive an optimal strategy., QC 20220302

We propose a hybrid classical-quantum approach for modeling transition probabilities in health and disability insurance. The modeling of logistic disability inception probabilities is formulated as a support vector regression problem. Using a quantum feature map, the data are mapped to quantum states belonging to a quantum feature space, where the associated kernel is determined by the inner product between the quantum states. This quantum kernel can be efficiently estimated on a quantum computer. We conduct experiments on the IBM Yorktown quantum computer, fitting the model to disability inception data from a Swedish insurance company., QC 20220127

We consider a finite impulse response system with centered independent sub-Gaussian design covariates and noise components that are not necessarily identically distributed. We derive non-asymptotic near-optimal estimation and prediction bounds for the least squares estimator of the parameters. Our results are based on two concentration inequalities on the norm of sums of dependent covariate vectors and on the singular values of their covariance operator that are of independent value on their own and where the dependence arises from the time shift structure of the time series. These results generalize the known bounds for the independent case., QC 20210423

We study a general class of fully coupled backward-forward stochastic differential equations of mean-field type (MF-BFSDE). We derive existence and uniqueness results for such a system under weak monotonicity assumptions and without the non-degeneracy condition on the forward equation. This is achieved by suggesting an implicit approximation scheme that is shown to converge to the solution of the system of MF-BFSDE. We apply these results to derive an explicit form of open-loop Nash equilibrium strategies for nonzero sum mean-field linear-quadratic stochastic differential games with random coefficients. These strategies are valid for any time horizon of the game., QC 20210323. QC 20211010

We consider the stochastic target problem of finding the collection of initial laws of a mean-field stochastic differential equation such that we can control its evolution to ensure that it reaches a prescribed set of terminal probability distributions, at a fixed time horizon. Here, laws are considered conditionally to the path of the Brownian motion that drives the system. This kind of problems is motivated by limiting behavior of interacting particles systems with applications in, for example, agricultural crop management. We establish a version of the geometric dynamic programming principle for the associated reachability sets and prove that the corresponding value function is a viscosity solution of a geometric partial differential equation. This provides a characterization of the initial masses that can be almost surely transported toward a given target, along the paths of a stochastic differential equation. Our results extend those of Soner and Touzi, Journal of the European Mathematical Society (2002) to our setting., QC 20201217

In this paper, the credit scoring problem is studied by incorporating networked information, where the advantages of such incorporation are investigated theoretically in two scenarios. Firstly, a Bayesian optimal filter is proposed to provide risk prediction for lenders assuming that published credit scores are estimated merely from structured financial data. Such prediction can then be used as a monitoring indicator for the risk management in lenders’ future decisions. Secondly, a recursive Bayes estimator is further proposed to improve the precision of credit scoring by incorporating the dynamic interaction topology of clients. It is shown theoretically that under the proposed evolution framework, the designed estimator has a higher precision than any efficient estimator, and the mean square errors are strictly smaller than the Cramér–Rao lower bound for clients within a certain range of scores. Finally, simulation results for a special case illustrate the feasibility and effectiveness of the proposed algorithms., QC 20200707

Life insurance cash flows become reserve dependent when contract conditions are modified during the contract term on condition that actuarial equivalence is maintained. As a result, insurance cash flows and prospective reserves depend on each other in a circular way, and it is a non-trivial problem to solve that circularity and make cash flows and prospective reserves well-defined. In Markovian models, the (stochastic) Thiele equation and the Cantelli Theorem are the standard tools for solving the circularity issue and for maintaining actuarial equivalence. This paper expands the stochastic Thiele equation and the Cantelli Theorem to non-Markovian frameworks and presents a recursive scheme for the calculation of multiple contract modifications., QC 20200826

This paper introduces a system of SDEs of mean-field type that models pedestrian motion. The system lets the pedestrians spend time at and move along walls by means of sticky boundaries and boundary diffusion. As an alternative to Neumann-type boundary conditions, sticky boundaries and boundary diffusion have a "smoothing" effect on pedestrian motion. When these effects are active, the pedestrian paths are semimartingales with the first-variation part absolutely continuous with respect to the Lebesgue measure dt rather than an increasing process (which in general induces a measure singular with respect to dt) as is the case under Neumann boundary conditions. We show that the proposed mean-field model for pedestrian motion admits a unique weak solution and that it is possible to control the system in the weak sense, using a Pontryagin-type maximum principle. We also relate the mean-field type control problem to the social cost minimization in an interacting particle system. We study the novel model features numerically, and we confirm empirical findings on pedestrian crowd motion in congested corridors., QC 20200729

Credit scoring is one of the key problems in financial risk managements. This paper studies the credit scoring problem based on the set-valued identification method, which is used to explain the relation between the individual attribute vectors and classification for the credit worthy and credit worthless lenders. In particular, system parameters are estimated by the set-valued identification algorithm based on a given recognition criteria. In order to illustrate the efficiency of the proposed method, practical experiments are conducted for credit card applicants of Australia and credit card holders from Taiwan, respectively. The empirical results show that the set-valued model has a higher prediction accuracy on both small and large numbers of data set compared with logistic regression model. Furthermore, parameters estimated by the set-valued identification method are more stable, which provide a meaningful and logical explanation for extracting factors that influence the borrowers’ credit scorings., QC 20200629

We consider an infinite horizon control problem for dynamics constrained to remain on a multidimensional junction with entry costs. We derive the associated system of Hamilton-Jacobi equations (HJ), prove the comparison principle and that the value function of the optimal control problem is the unique viscosity solution of the HJ system. This is done under the usual strong controllability assumption and also under a weaker condition, coined 'moderate controllability assumption'., QC 20200416

In this article, a profit optimization between electricity producers is formulated and solved. The problem is described by a linear jump-diffusion system of conditional mean-field type where the conditioning is with respect to common noise and a quadratic cost functional involving the second moment, the square of the conditional expectation of the control actions of the producers. We provide semi-explicit solution of the corresponding mean-field-type game problem with common noise. The equilibrium strategies are in state-and-conditional mean-field feedback form, where the mean-field term is the conditional price given the realization of the global uncertainty. The methodology is extended to a situation of incomplete information mean-field-type game in which each producer knows its own type but not the types of the other producers. We compute the Bayesian mean-field-type equilibrium in a semi-explicit way and show that it is not ex post resilient., QC 20211001

This article presents a class of Stackelberg mean-field-type games with multiple leaders and multiple followers. The decision-makers act in sequential order with informational differences. The state dynamics is driven by jump-diffusion processes and the cost function is non-quadratic and has a polynomial structure. The structures of Stackelberg strategies and costs of the leaders and followers are given in a semi-explicit way in state-and- mean-fieldtype feedback form. A sufficiency condition is provided using an infinite dimensional partial integro-differential system. The methodology is extended to multi-level hierarchical systems. It is shown that not only the set of decision-makers per level matters but also the number of hierarchical levels plays a key role in the global performance of the system. We also identify specific range of parameters for which the Nash equilibrium coincides with the hierarchical solution independently of the number of layers and the order of play., QC 20210720

In this paper we examine mean-field-type games in blockchain-based distributed power networks with several different entities: investors, consumers, prosumers, producers and miners. Under a simple model of jump-diffusion and regime switching processes, we identify risk-aware mean-field-type optimal strategies for the decision-makers., QC 20200909

This work examines the solvability of fractional conditional mean-field-type games. The evolution of the state is described by a time-fractional stochastic dynamics driven by jump-diffusion-regime switching Gauss-Volterra processes which include fractional Brownian motion and multi-fractional Brownian motion. The cost functional is non-quadratic and includes a fractional-integral of an higher order polynomial. We provide semi-explicitly the equilibrium strategies in state-and-conditional mean-field-type feedback form for all decision-makers., QC 20200702

In this paper, we investigate a credit rating problem based on the network of trading information (NoTI). First, several popular tools, such as assortativity analysis, community detection and centrality measurement, are introduced for analyzing the topology structures and properties of the NoTI. Then, the correlation between the characteristics of the network and the credit ratings is investigated to illustrate the feasibility of credit risk analysis based on the NoTI. Sovereign rating based on the world trade network is analyzed as a case study. The correlation between the centrality metrics and the sovereign ratings conducted by Standard & Poor's clearly shows that highly ranked economies with vigorous economic trading links usually have higher credit ratings. Finally, a simulation is conducted to illustrate the degree of improvement in credit rating prediction accuracy if the NoTI is considered as an additional attribute., QC 20190904

This paper suggests a model for the motion of tagged pedestrians: Pedestrians moving towards a specified targeted destination, which they are forced to reach. It aims to be a decision-making tool for the positioning of fire fighters, security personnel and other services in a pedestrian environment. Taking interaction with the surrounding crowd into account leads to a differential nonzero-sum game model where the tagged pedestrians compete with the surrounding crowd of ordinary pedestrians. When deciding how to act, pedestrians consider crowd distribution-dependent effects, like congestion and crowd aversion. Including such effects in the parameters of the game, makes it a mean-field type game. The equilibrium control is characterized, and special cases are discussed. Behavior in the model is studied by numerical simulations., QC 20190319

We establish existence of controlled Markov chain of mean-field type with unbounded jump intensities by means of a fixed point argument using the Wasserstein distance. Furthermore, we suggest conditions for existence of an optimal control and a saddle-point for respectively a control problem and a zero-sum differential game associated with risk sensitive payoff functionals of mean-field type. The conditions are derived using a Markov chain entropic backward SDE approach., QC 20190319

We establish existence of Markov chains of mean-field type with unbounded jump intensities by means of a fixed point argument using the total variation distance. We further show existence of nearly-optimal controls and, using a Markov chain backward SDE approach, we suggest conditions for existence of an optimal control and a saddle-point for respectively a control problem and a zero-sum differential game associated with payoff functionals of mean-field type, under dynamics driven by such Markov chains of mean-field type., Not duplicate with DiVA 1269929QC 20230202

Point and interval estimation of future disability inception and recovery rates is predominantly carried out by combining generalized linear models with time series forecasting techniques into a two-step method involving parameter estimation from historical data and subsequent calibration of a time series model. This approach may lead to both conceptual and numerical problems since any time trend components of the model are incoherently treated as both model parameters and realizations of a stochastic process. We suggest that this general two-step approach can be improved in the following way: First, we assume a stochastic process form for the time trend component. The corresponding transition densities are then incorporated into the likelihood, and the model parameters are estimated using the Expectation-Maximization algorithm. We illustrate the modeling procedure by fitting the model to Swedish disability claims data., QC 20180618

We extend the class of pedestrian crowd models introduced by Lachapelle and Wolfram [Transp. Res. B: Methodol., 45 (2011), pp. 1572–1589] to allow for nonlocal crowd aversion and arbitrarily but finitely many interacting crowds. The new crowd aversion feature grants pedestrians a “personal space” where crowding is undesirable. We derive the model from a particle picture and treat it as a mean-field type game. Solutions to the mean-field type game are characterized via a Pontryagin-type maximum principle. The behavior of pedestrians acting under nonlocal crowd aversion is illustrated by a numerical simulation., QC 20180320

We establish existence of controlled Markov chain of mean-field type with unbounded jump intensities by means of a fixed point argument using the Wasserstein distance. Using a Markov chain entropic backward SDE approach, we further suggest conditions for existence of an optimal control and a saddle-point for respectively a control problem and a zero-sum differential game associated with risk sensitive payoff functionals of mean-field type., QC 20181212

We establish existence of Markov chains of mean-field type with unbounded jump intensities by means of a fixed point argument using the Total Variation distance. We further show existence of nearly-optimal controls and, using a Markov chain backward SDE approach, we suggest conditions for existence of an optimal control and a saddle-point for respectively a control problem and a zero-sum differential game associated with payoff functionals of mean-field type, under dynamics driven by such Markov chains of mean-field type., QC 20181212

In this paper, we deal with the solutions of systems of PDEs with bilateral interconnected obstacles of min-max and max-min types. These systems arise naturally in stochastic switch-in zero-sum game problems. We show that when the switching costs of one side are regular, the solutions of the min-max and max-min systems coincide. Then, this common viscosity solution is related to a multi-dimensional doubly reflected BSDE with bilateral interconnected obstacles. Finally, its relationship with the values of a zero-sum switching game is studied., QC 20170517

A mean-field-type game is a game in which the instantaneous payoffs and/or the state dynamics functions involve not only the state and the action profile but also the joint distributions of state-action pairs. This article presents some engineering applications of mean-field-type games including road traffic networks, multi-level building evacuation, millimeter wave wireless communications, distributed power networks, virus spread over networks, virtual machine resource management in cloud networks, synchronization of oscillators, energy-efficient buildings, online meeting and mobile crowdsensing., QC 20210927

We study a version of the functional Hodrick-Prescott filter in the case when the associated operator is not necessarily compact but merely closed and densely defined with closed range. We show that the associated optimal smoothing operator preserves the structure obtained in the compact case when the underlying distribution of the data is Gaussian., QC 20160519

We establish a stochastic maximum principle (SMP) for control problems of partially observed diffusions of mean-field type with risk-sensitive performance functionals., QC 20160205

This is a short introduction to some basic aspects of statistical estimation techniques known as graduation technique in life and disability insurance., QC 20160520

We study a class of dynamic decision problems of mean-field type with time-inconsistent cost functionals and derive a stochastic maximum principle to characterize sub-game perfect equilibrium points. Subsequently, this approach is extended to a mean-field game to construct decentralized strategies and obtain an estimate of their performance., QC 20160303

We suggest a unified approach to claims reserving for life insurance policies with reserve-dependent payments driven by multi-state Markov chains. The associated prospective reserve is formulated as a recursive utility function using the framework of backward stochastic differential equations (BSDE). We show that the prospective reserve satisfies a nonlinear Thiele equation for Markovian BSDEs when the driver is a deterministic function of the reserve and the underlying Markov chain. Aggregation of prospective reserves for large and homogeneous insurance portfolios is considered through mean-field approximations. We show that the corresponding prospective reserve satisfies a BSDE of mean-field type and derive the associated nonlinear Thiele equation., QC 20160518

This work introduces a simple mean-field network game that captures some of the key dynamic features of crowd and pedestrian flows in multi-level building evacuations. It considers a route choice by finite number of strategic agents. Each agent state is represented by a simple first order dynamical system. Each agent measures its local congestion measure based on its location in the building. Including the local congestion term and its evolution along the path causes a sort of dispersion of the flow: the agents will try to avoid high density areas in order to reduce their overall walking costs and queuing cost at the exits. Each agent will move to one the closest exits that is safer and that has less congestion through the path. The dynamics of lower layer floors are influenced not only by the agents in that floor but also by the incoming flow from the upper layers through the stairs leading to interacting flows between the floors. Numerics and simulations are carried out to illustrate mean-field equilibria of the evacuation process., QC 20161129

We propose a stochastic semi-Markovian framework for disability modelling in a multi-period discrete-time setting. The logistic transforms of disability inception and recovery probabilities are modelled by means of stochastic risk factors and basis functions, using counting processes and generalized linear models. The model for disability inception also takes IBNR claims into consideration. We fit various versions of the models into Swedish disability claims data., QC 20150113. Updated from e-pub ahead of print.

We study a general class of nonlinear second-order variational inequalities with interconnected bilateral obstacles, related to a multiple modes switching game. Under rather weak assumptions, using systems of penalized unilateral backward SDEs, we construct a continuous viscosity solution of polynomial growth. Moreover, we establish a comparison result which in turn yields uniqueness of the solution., QC 20150508

We formulate and solve a finite horizon full balance sheet of a two-mode optimal switching problem related to trade-off strategies between expected profit and cost yields. Given the current mode, this model allows for either a switch to the other mode or termination of the project, and this happens for both sides of the balance sheet. A novelty in this model is that the related obstacles are nonlinear in the underlying yields, whereas, they are linear in the standard optimal switching problem. The optimal switching problem is formulated in terms of a system of Snell envelopes for the profit and cost yields which act as obstacles to each other. We prove the existence of a continuous minimal solution of this system using an approximation scheme and fully characterize the optimal switching strategy., QC 20150918

In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle for optimal control of stochastic differential equations of mean-field type, in which the drift and the diffusion coefficients as well as the performance functional depend not only on the state and the control but also on the mean of the distribution of the state. Our result extends to optimal control problems for non-Markovian dynamics which may be time-inconsistent in the sense that the Bellman optimality principle does not hold. For a general action space a Peng's type stochastic maximum principle is derived, specifying the necessary conditions for optimality. Two examples are carried out to illustrate the proposed risk-sensitive mean-field type under linear stochastic dynamics with exponential quadratic cost function. Explicit characterizations are given for both mean-field free and mean-field risk-sensitive models., QC 20151202

This article examines mean-field games for marriage. The results support the argument that optimizing the long-term wellbeing through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple's network on their feeling states and their well-being., QC 20140624

We consider a large, homogeneous portfolio of life or disability annuity policies. The policies are assumed to be independent conditional on an external stochastic process representing the economic-demographic environment. Using a conditional law of large numbers, we establish the connection between claims reserving and risk aggregation for large portfolios. Further, we derive a partial differential equation for moments of present values. Moreover, we show how statistical multi-factor intensity models can be approximated by one-factor models, which allows for solving the PDEs very efficiently. Finally, we give a numerical example where moments of present values of disability annuities are computed using finite-difference methods and Monte Carlo simulations., QC 20150209. Updated from manuscript to article in journal.

We consider the problem of switching a large number of production lines between two modes, high-production and low-production. The switching is based on the optimal expected profit and cost yields of the respective production lines, and considers both sides of the balance sheet. Furthermore, the production lines are all assumed to be interconnected through a coupling term, which is the average of all optimal expected yields. Intuitively, this means that each individual production line is compared to the average of all its peers which acts as a benchmark. Due to the complexity of the problem, we consider the aggregated optimal expected yields, where the coupling term is approximated with the mean of the optimal expected yields. This turns the problem into a two-modes optimal switching problem of mean-field type, which can be described by a system of Snell envelopes where the obstacles are interconnected and nonlinear. The main result of the paper is a proof of a continuous minimal solution to the system of Snell envelopes, as well as the full characterization of the optimal switching strategy., Updated from "Manuscript" to "Article". QC 20150918

We suggest an optimality criterion, for choosing the best smoothing parameters for an extension of the so-called Hodrick-Prescott Multivariate (HPMV) filter. We show that this criterion admits a whole set of optimal smoothing parameters, to which belong the widely used noise-to-signal ratios. We also propose explicit consistent estimators of these noise-to-signal ratios, which in turn yield a new performant method to estimate the output gap., QC 20110503

We consider a finite horizon optimal stopping problem related to trade-off strategies between expected profit and cost cash flows of an investment under uncertainty. The optimal problem is first formulated in terms of a system of Snell envelopes for the profit and cost yields which act as obstacles to each other. We then construct both a minimal solution and a maximal solution using an approximation scheme of the associated system of reflected backward stochastic differential equations (SDEs). We also address the question of uniqueness of solutions of this system of SDEs. When the dependence of the cash flows on the sources of uncertainty, such as fluctuation market prices, assumed to evolve according to a diffusion process, is made explicit, we obtain a connection between these solutions and viscosity solutions of a system of variational inequalities with interconnected obstacles., QC 20120125

In this note, nonlinear stochastic partial differential equations (SPDEs) with continuous coefficients are studied. Via the solutions of backward doubly stochastic differential equations (BDSDEs) with continuous coefficients, we provide an existence result of stochastic viscosity sub- and super-solutions to this class of SPDEs. Under some stronger conditions, we prove the existence of stochastic viscosity solutions. (C) 2010 Elsevier Inc. All rights reserved.

We study the optimal control for stochastic differential equations (SDEs) of mean-field type, in which the coefficients depend on the state of the solution process as well as of its expected value. Moreover, the cost functional is also of mean-field type. This makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. For a general action space a Peng's-type stochastic maximum principle (Peng, S.: SIAM J. Control Optim. 2(4), 966-979, 1990) is derived, specifying the necessary conditions for optimality. This maximum principle differs from the classical one in the sense that here the first order adjoint equation turns out to be a linear mean-field backward SDE, while the second order adjoint equation remains the same as in Peng's stochastic maximum principle., QC 20110816

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We suggest an explicit solution to the graduation problem that aims at designing an optimal curve fit which simultaneously behaves as a smoothing B-spline in each time interval and as the Hodrick-Prescott filter in the knots We also outline its numerical performance and compare it to the existing estimates of the standard Hodrick-Prescott filter., QC 20120125