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Mathematics
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Stochastic Optimization Methods in Economics, Finance and Insurance
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Stochastic Optimization Methods in Economics, Finance and Insurance

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Financial Mathematics".

Deadline for manuscript submissions: closed (31 May 2021) | Viewed by 14878

Special Issue Editors

Prof. Dr. Claudia Ceci

E-Mail Website
Guest Editor
Department of Economics, University of Chieti-Pescara, 66013 Abruzzo, Italy
Interests: stochastic processes; filtering; optimal control; optimal stopping; BSDEs; applications in finance; insurance and economics
Dr. Matteo Brachetta

E-Mail Website
Guest Editor
Department of Mathematics, Politecnico of Milan, Milan, Italy
Interests: optimal reinsurance and investment; stochastic control problems and applications in finance; insurance and economics

Special Issue Information

Dear Colleagues,

Stochastic optimization finds numerous and various applications in economics, finance, and insurance. Among these, we may cite optimal portfolio selection, optimal reinsurance, and investment problems, utility maximization and application to valuation of financial and insurance derivatives, optimal management of pension fund and public debt, and risk measures. This Special Issue aims at collecting original research papers or comprehensive reviews on the theory and applications of dynamic stochastic optimization in economics, finance and insurance. Advanced mathematical tools have been employed to handle with these problems including viscosity solutions approach, martingale methods, backward stochastic differential equations (BSDEs), partial differential equations (PDEs), convex duality, filtering techniques, and various numerical methods. Applications different from stochastic optimization will be possibly considered.

Prof. Dr. Claudia Ceci
Dr. Matteo Brachetta
Guest Editors

Manuscript Submission Information

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Keywords

  • Stochastic control
  • Optimal reinsurance
  • Utility maximization
  • Financial and insurance derivatives
  • Backward stochastic differential equations
  • Partial information

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Published Papers (6 papers)

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Research

27 pages, 723 KiB  
Article
Optimal Investment and Proportional Reinsurance in a Regime-Switching Market Model under Forward Preferences
by Katia Colaneri, Alessandra Cretarola and Benedetta Salterini
Mathematics 2021, 9(14), 1610; https://doi.org/10.3390/math9141610 - 8 Jul 2021
Cited by 3 | Viewed by 2228
Abstract
In this paper, we study the optimal investment and reinsurance problem of an insurance company whose investment preferences are described via a forward dynamic exponential utility in a regime-switching market model. Financial and actuarial frameworks are dependent since stock prices and insurance claims [...] Read more.
In this paper, we study the optimal investment and reinsurance problem of an insurance company whose investment preferences are described via a forward dynamic exponential utility in a regime-switching market model. Financial and actuarial frameworks are dependent since stock prices and insurance claims vary according to a common factor given by a continuous time finite state Markov chain. We construct the value function and we prove that it is a forward dynamic utility. Then, we characterize the optimal investment strategy and the optimal proportional level of reinsurance. We also perform numerical experiments and provide sensitivity analyses with respect to some model parameters. Full article
(This article belongs to the Special Issue Stochastic Optimization Methods in Economics, Finance and Insurance)
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20 pages, 665 KiB  
Article
Short-Term Interest Rate Estimation by Filtering in a Model Linking Inflation, the Central Bank and Short-Term Interest Rates
by Flavia Antonacci, Cristina Costantini and Marco Papi
Mathematics 2021, 9(10), 1152; https://doi.org/10.3390/math9101152 - 20 May 2021
Cited by 2 | Viewed by 2405
Abstract
We consider the model of Antonacci, Costantini, D’Ippoliti, Papi (arXiv:2010.05462 [q-fin.MF], 2020), which describes the joint evolution of inflation, the central bank interest rate, and the short-term interest rate. In the case when the diffusion coefficient does not depend on the central bank [...] Read more.
We consider the model of Antonacci, Costantini, D’Ippoliti, Papi (arXiv:2010.05462 [q-fin.MF], 2020), which describes the joint evolution of inflation, the central bank interest rate, and the short-term interest rate. In the case when the diffusion coefficient does not depend on the central bank interest rate, we derive a semi-closed valuation formula for contingent derivatives, in particular for Zero Coupon Bonds (ZCBs). By using ZCB yields as observations, we implement the Kalman filter and obtain a dynamical estimate of the short-term interest rate. In turn, by this estimate, at each time step, we calibrate the model parameters under the risk-neutral measure and the coefficient of the risk premium. We compare the market values of German interest rate yields for several maturities with the corresponding values predicted by our model, from 2007 to 2015. The numerical results validate both our model and our numerical procedure. Full article
(This article belongs to the Special Issue Stochastic Optimization Methods in Economics, Finance and Insurance)
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20 pages, 412 KiB  
Article
Optimal Reinsurance Problem under Fixed Cost and Exponential Preferences
by Matteo Brachetta and Claudia Ceci
Mathematics 2021, 9(4), 295; https://doi.org/10.3390/math9040295 - 3 Feb 2021
Cited by 3 | Viewed by 2381
Abstract
We investigate an optimal reinsurance problem for an insurance company taking into account subscription costs: that is, a constant fixed cost is paid when the reinsurance contract is signed. Differently from the classical reinsurance problem, where the insurer has to choose an optimal [...] Read more.
We investigate an optimal reinsurance problem for an insurance company taking into account subscription costs: that is, a constant fixed cost is paid when the reinsurance contract is signed. Differently from the classical reinsurance problem, where the insurer has to choose an optimal retention level according to some given criterion, in this paper, the insurer needs to optimally choose both the starting time of the reinsurance contract and the retention level to apply. The criterion is the maximization of the insurer’s expected utility of terminal wealth. This leads to a mixed optimal control/optimal stopping time problem, which is solved by a two-step procedure: first considering the pure-reinsurance stochastic control problem and next discussing a time-inhomogeneous optimal stopping problem with discontinuous reward. Using the classical Cramér–Lundberg approximation risk model, we prove that the optimal strategy is deterministic and depends on the model parameters. In particular, we show that there exists a maximum fixed cost that the insurer is willing to pay for the contract activation. Finally, we provide some economical interpretations and numerical simulations. Full article
(This article belongs to the Special Issue Stochastic Optimization Methods in Economics, Finance and Insurance)
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25 pages, 739 KiB  
Article
Optimal Exploitation of a General Renewable Natural Resource under State and Delay Constraints
by M’hamed Gaïgi, Idris Kharroubi and Thomas Lim
Mathematics 2020, 8(11), 2053; https://doi.org/10.3390/math8112053 - 18 Nov 2020
Viewed by 1598
Abstract
In this work, we study an optimization problem arising in the management of a natural resource over an infinite time horizon. The resource is assumed to evolve according to a logistic stochastic differential equation. The manager is allowed to harvest the resource and [...] Read more.
In this work, we study an optimization problem arising in the management of a natural resource over an infinite time horizon. The resource is assumed to evolve according to a logistic stochastic differential equation. The manager is allowed to harvest the resource and sell it at a stochastic market price modeled by a geometric Brownian process. We assume that there are delay constraints imposed on the decisions of the manager. More precisely, starting harvesting order and selling order are executed after a delay. By using the dynamic programming approach, we characterize the value function as the unique solution to an original partial differential equation. We complete our study with some numerical illustrations. Full article
(This article belongs to the Special Issue Stochastic Optimization Methods in Economics, Finance and Insurance)
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24 pages, 392 KiB  
Article
The Optimal Control of Government Stabilization Funds
by Abel Cadenillas and Ricardo Huamán-Aguilar
Mathematics 2020, 8(11), 1975; https://doi.org/10.3390/math8111975 - 6 Nov 2020
Cited by 2 | Viewed by 2142
Abstract
We study the optimal control of a government stabilization fund, which is a mechanism to save money during good economic times to be used in bad economic times. The objective of the fund manager is to keep the fund as close as possible [...] Read more.
We study the optimal control of a government stabilization fund, which is a mechanism to save money during good economic times to be used in bad economic times. The objective of the fund manager is to keep the fund as close as possible to a predetermined target. Accordingly, we consider a running cost associated with the difference between the actual fiscal fund and the fund target. The fund manager exerts control over the fund by making deposits in or withdrawals from the fund. The withdrawals are used to pay public debt or to finance government programs. We obtain, for the first time in the literature, the optimal band for the government stabilization fund. Our results are of interest to practitioners. For instance, we find that the higher the volatility, the larger the size of the optimal band. In particular, each country and state should have its own optimal fund band, in contrast to the “one-size-fits-all” approach that is often used in practice. Full article
(This article belongs to the Special Issue Stochastic Optimization Methods in Economics, Finance and Insurance)
23 pages, 516 KiB  
Article
Mean-Variance Portfolio Selection with Tracking Error Penalization
by William Lefebvre, Grégoire Loeper and Huyên Pham
Mathematics 2020, 8(11), 1915; https://doi.org/10.3390/math8111915 - 1 Nov 2020
Cited by 10 | Viewed by 2689
Abstract
This paper studies a variation of the continuous-time mean-variance portfolio selection where a tracking-error penalization is added to the mean-variance criterion. The tracking error term penalizes the distance between the allocation controls and a reference portfolio with same wealth and fixed weights. Such [...] Read more.
This paper studies a variation of the continuous-time mean-variance portfolio selection where a tracking-error penalization is added to the mean-variance criterion. The tracking error term penalizes the distance between the allocation controls and a reference portfolio with same wealth and fixed weights. Such consideration is motivated as follows: (i) On the one hand, it is a way to robustify the mean-variance allocation in the case of misspecified parameters, by “fitting" it to a reference portfolio that can be agnostic to market parameters; (ii) On the other hand, it is a procedure to track a benchmark and improve the Sharpe ratio of the resulting portfolio by considering a mean-variance criterion in the objective function. This problem is formulated as a McKean–Vlasov control problem. We provide explicit solutions for the optimal portfolio strategy and asymptotic expansions of the portfolio strategy and efficient frontier for small values of the tracking error parameter. Finally, we compare the Sharpe ratios obtained by the standard mean-variance allocation and the penalized one for four different reference portfolios: equal-weights, minimum-variance, equal risk contributions and shrinking portfolio. This comparison is done on a simulated misspecified model, and on a backtest performed with historical data. Our results show that in most cases, the penalized portfolio outperforms in terms of Sharpe ratio both the standard mean-variance and the reference portfolio. Full article
(This article belongs to the Special Issue Stochastic Optimization Methods in Economics, Finance and Insurance)
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