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In the wave energy converter (WEC) optimal control problem, the well-developed model predictive control (MPC) faces the trade-off between energy extraction performance and online computation burden when choosing the length of optimization horizon. In this work, a novel MPC problem formulation is proposed, which includes a terminal value function and a terminal constraint set. The terminal value function is derived by further calculating the system trajectory beyond the optimization horizon based on a pre-chosen "rollout" policy, which incorporates more future information and improves energy extraction. The linear reactive control is chosen as the rollout policy, under which a policy improvement theorem of the WEC system is derived. The terminal constraint set is a simple control invariant set that ensures the recursive feasibility of MPC. Extensive simulations show that the proposed reactive rollout MPC can achieve close-to-optimal performance with a very short optimization horizon, reducing the online computation burden significantly.

Terminal value problems of fractional nonlinear systems are studied in this paper. The existence and uniqueness are given. The regularity of the solution is obtained in the weighted spaces. Discretized piecewise polynomial collocation methods are proposed on the graded mesh. A convergence analysis and the order are presented. Numerical examples for supporting theoretical results and applications for population models are illustrated.

Participating (or with-profit) life insurance contracts play an important role in private old-age provision in many countries. Life insurers pool the assets and liabilities of a heterogeneous portfolio of such contracts and typically perform some return smoothing in the collective investment. Participating contracts were historically equipped with a cliquet-style (year-to-year) guarantee. The current low interest rate environment and regulatory requirements have forced life insurers to develop new product designs with lower and/or different types of guarantees. However, observed demand as well as the findings of several studies show that (year-to-year) guarantees are (subjectively) highly attractive for long-term investors. In this paper, we show that return smoothing alone (that is, without guarantees) can significantly increase the attractiveness for such investors. Most importantly, we show that many (loss averse) long-term investors will even prefer products without guarantee but with smoothed returns over other products with guarantee features. The results hold for long-term investors who not only consider the terminal value but at least partially also evaluate potential annual changes in the account value (even if such changes only have a rather low impact on the decision). Additionally, we show that the descriptive model used in this paper is able to explain the popularity of traditional participating life insurance products in Germany providing further evidence that long-term investors consider potential annual value chances already when making the investment decision.

We consider terminal value problems for time-space fractional pseudo-parabolic equation subjected to a final/terminal value condition. In fact, fractional orders α , s are not exactly known in modeling. These are determined experimentally. The main purpose is to investigate the continuity of the solution with respect to the fractional order α ∈ ( 0 , 1 ) , which accordingly answer the question: does ρ α n → ρ α in an appropriate sense as α n → α ? Firstly, a formulation for integral solutions has been established, which based on Laplace transform and spectral expansion of the Mittag-Leffler operators. Then, the desired continuity will be obtained by making use of resolvent representations of the Mittag-Leffler operators on Hankel's contour. Finally, we present some numerical examples to illustrate the proposed theory.

This manuscript deals with a class of Katugampola implicit fractional differential equations in b -metric spaces. The results are based on the α − φ -Geraghty type contraction and the fixed point theory. We express an illustrative example.

In any context where a discounted cash flow valuation is required, there is the issue of estimating the continuing value. The most common way to do that is to assume that by the terminal horizon the company is in a steady state and is growing at a constant rate. The issue is how to handle inflation. The problem is that it is often done wrong and the impact is typically material. Because there remains significant confusion, in this paper we simplify the analysis by isolating the two key issues and providing example calculations. We show that even at the current 2% level proper treatment of inflation has a sizeable impact on valuation. If inflation were to accelerate as a result of current monetary and fiscal policies, the significance of this issue will increase.

In this article, explicit representation of solution for the Hamilton–Jacobi–Bellman (HJB) equation associated with the portfolio optimization problem for an investor who seeks to maximize the expected power (CRRA) utility of the terminal wealth in a defined-contribution pension plan under a constant elasticity of variance model is derived based on the application of the Lie symmetry method to the partial differential equation and its associated terminal condition. Compared with the ingenious ansatz techniques used before, here we present a group theoretical analysis of the terminal value problem for the solution following the algorithmic procedure of the Lie symmetry analysis. It shows that the interesting properties of the group structures of the original HJB equation and its successive similarity reduced equations lead to an elegant resolution of the problem. Moreover, we identify the meaningful range of risk aversion coefficient which is ignored in the previous work. At last, the properties and sensitivity analysis of the derived optimal strategy are demonstrated by numerical simulations and several figures. The method used here is quite general and can be applied to other equations obtained in financial mathematics.

In this paper we investigate the management of a defined benefit pension plan under a model with random coefficients. The objective of the pension sponsor is to minimize the solvency risk, contribution risk and the expected terminal value of the unfunded actuarial liability. By measuring the solvency risk in terms of the variance of the terminal unfunded actuarial liability, we formulate the problem as a mean-variance problem with an additional running cost. With the help of a system of backward stochastic differential equations, we derive a time-consistent equilibrium strategy towards investment and contribution rate. The obtained equilibrium strategy turns out to be a good candidate for a stable contribution plan. When the interest rate is given by the Vasicek model and all other coefficients are deterministic, we obtain closed-form solutions of the equilibrium strategy and efficient frontier.

The increase of MSMEs in the food and beverage industry recently experiencing significant growth, especially during the Covid-19 pandemic. According to statistical data released by the Badan Pusat Statistik (BPS) in November 2020, the food industry dominated Micro and Small businesses in 2019 for 36.23%. The increasing number of MSME businesses in this sector becomes an opportunity for the processing services industry (contract manufacturer) to help MSMEs with all limitations. This study conducted a case study on PT. Krispindo as a company engaged in processing services (contract manufacturer) in the snack sector. This research aims to assess (valuation) new business proposed by PT. Krispindo in terms of optimal use of debt and equity for the company and also investment returns that can be given to investors. In addition, this research also aims to assist the company in making decisions for the following period project, decision to continue or discontinue the business. This study used optimal Cost of Capital (WACC) and Debt-to-Equity Ratio (DER) in setting optimal business capital. To measure investment return expectations for investors, the study used the company's Net Present Value (NPV), Free Cash Flow to Firm (FCFF) and Internal Rate of Return (IRR) approaches. To find out whether or not the business is further, this study uses Terminal Value Asset (TVA) and On Going Concern Value from the business obtained when the project ending. The results prove using debt in capital has more benefit for the company and the business can continue after the projection period ends. Keywords: New Business Valuation (NPV), Debt-to-equity ratio (DER), Average Cost of Capital (WACC), Free Cash Flow to Firm (FCFF), Internal Rate of Return (IRR), Terminal Value Asset (TVA) and On Going Concern Value

Indian mutual fund industry is in upward trend as the assets are increasing under management of various fund houses. It is found that mutual investment is less risky than investments in stocks which are therefore a safer option for investors who avoid risk. It has been observes from the market that most of the investors ae not aware of the benefits of mutual funds. This research paper has given emphasis on the awareness level of respondents towards mutual fund and also an attempt has made to identify various variables responsible for investors to invest in mutual funds. Findings of the research will help the companies to identify the areas of improvement required to create more awareness among mutual fund investors. A sample size of 250 comprising of different profile investors considered for the survey and for that judgment sampling procedure followed. The sixteen variables considered for the study that influences the attitude towards mutual fund has taken and analyzed with the help of factor analysis through SPSS and four factors generated which are risk, belief, terminal value and self-concept. These ae the few factors like risk, belief, terminal value and self-concept which has considered by the customers during their investment in mutual funds. Keywords: Mutual, Fund, Factor, Eigen, Value.

The present work has the objective of analyzing what generates or maximizes the market value of the financial groups listed on the Mexican Stock Exchange (BMV), given an increase in either growth or profitability. For this, the terminal value or perpetuity developed by Gordon and Shapiro is considered and used in the valuation methodology for discounted dividend flows, as well as financial information for the period 2014 to 2018. In addition, the analysis proposed by Mass is applied to assess the potential for growth and yield. It is determined that the value generated by the growth is greater than that obtained by the increase in profitability in the five financial institutions analyzed. The results would still imply that potential growth exists, that the financial institutions are not yet fully mature or developed and/or not operate in a mature or developed market, so that Fintech strategies to promote growth would be better valued by the market.

Spectral collocation method is proposed to solve Caputo fractional terminal value problem. The main idea of the proposed method is to solve the corresponding nonlinear weakly singular Volterra-Fredholm integral equation. The key step in presented method is to transform the nonlinear integral kernels to linear integral kernels by a functional transformation. Then, the integral terms can be calculated exactly by Gauss quadrature formula. The provided convergence analysis shows that the presented method has spectral convergency. Theoretical results are confirmed by numerical experiments. The presented method makes some improvements to the existed methods.

A class of tempered fractional differential equations with terminal value problems are investigated in this paper. Discretized collocation methods on piecewise polynomials spaces are proposed for solving these equations. Regularity results are constructed on weighted spaces and convergence order is studied. Several examples are supported the theoretical parts and compared with other methods.

In this paper we consider two cases of optimal implementation delay of taxation with trade-off under spectrally negative Levy insurance risk processes. In the first case, we assume that the insurance company starts to pay tax only when its surplus level reaches a certain level, and at the termination time of the business there is a terminal value incurred to the company. A method is developed to determine the optimal starting-tax surplus level at which the total expected discounted value of all tax payments up to the termination time plus the discounted terminal value is maximized. In the second case, the company still pays tax subject to a starting-tax surplus level, but with capital injections to prevent bankruptcy. The total expected discounted value of tax payments minus the total discounted capital injection costs is maximized to determine the optimal starting-tax surplus level. Numerical examples are given at the end to illustrate the existence of positive optimal starting-tax surplus levels for both cases considered in this paper.

To solve the problem of convergence of controlled objects in dynamic game problems with the terminal payoff function, the author proposes a method that systematically uses the Fenchel–Moreau ideas as applied to the general scheme of the method of resolving functions. The essence of the method is that the resolving function can be expressed in terms of the function conjugate to payoff function and, using the involution of the conjugation operator for a convex closed function, a guaranteed estimate of the terminal value of the payoff function is obtained, which can be presented in terms of the payoff value at the initial instant of time and integral of the resolving function. The concepts of upper and lower resolving functions of two types are introduced and sufficient conditions for a guaranteed result in a differential game with a terminal payoff function are obtained for the case where the Pontryagin condition does not hold. Two schemes of the method of resolving functions are considered, the corresponding control strategies are generated, and guaranteed times are compared. The results are illustrated by a model example.

In this paper we consider one dimensional mean-field backward stochastic differential equations (BSDEs) under weak assumptions on the coefficient. Unlike [3], the generator of our mean-field BSDEs depends not only on the solution (Y, Z) but also on the law PY of Y. The first part of the paper is devoted to the existence and uniqueness of solutions in Lp, 1 < p ≤ 2, where the monotonicity conditions are satisfied. Next, we show that if the generator f is uniformly continuous in (μ, y, z), uniformly with respect to (t, ω), and if the terminal value ξ belongs to Lp(Ω, F, P) with 1 < p ≤ 2, the mean-field BSDE has a unique Lp solution.

The work reported in this paper deals with the study of a coupled system for fractional terminal value problems involving ψ-Hilfer fractional derivative. The existence and uniqueness theorems to the problem at hand are investigated. Besides, the stability analysis in the Ulam–Hyers sense of a given system is studied. Our discussion is based upon known fixed point theorems of Banach and Krasnoselskii. Examples are also provided to demonstrate the applicability of our results.

The case is based on the investment decision faced by the fund manager of Pakistan Islamic Pension Fund (PIPF), Manal Iqbal, at a leading asset management company, MCB Arif Habib Savings and Investment Limited (MCBAH). In early April 2015, Manal was asked by the chief investment officer of the company to evaluate Millat Tractors Limited (MTL) as a potential investment for PIPF to gain exposure to the agricultural sector of Pakistan. She directed her research team to prepare a valuation report for the MTL stock and reflected on the strategic position of her pension fund for the investment committee meeting on 27 April 2015.

This paper is concerned with the mathematical analysis of terminal value problems (TVP) for a stochastic nonclassical diffusion equation, where the source is assumed to be driven by classical and fractional Brownian motions (fBms). Our two problems are to study in the sense of well-posedness and ill-posedness meanings. Here, a TVP is a problem of determining the statistical properties of the initial data from the final time data. In the case [Formula: see text], where [Formula: see text] is the fractional order of a Laplace operator, we show that these are well-posed under certain assumptions. We state a definition of ill-posedness and obtain the ill-posedness results for the problems when [Formula: see text]. The major analysis tools in this paper are based on properties of stochastic integrals with respect to the fBm.

In this paper, we study two terminal value problems (TVPs) for stochastic bi-parabolic equations perturbed by standard Brownian motion and fractional Brownian motion with Hurst parameter h ∈ ( 1 2 , 1 ) separately. For each problem, we provide a representation for the mild solution and find the space where the existence of the solution is guaranteed. Additionally, we show clearly that the solution of each problem is not stable, which leads to the ill-posedness of each problem. Finally, we propose two regularization results for both considered problems by using the filter regularization method.