Numerical methods for optimal dividend payment and investment strategies of regime-switching jump diffusion models with capital injections
This work focuses on numerical methods for finding optimal investment, dividend payment, and capital injection policies to maximize the present value of the difference between the cumulative dividend payment and the possible capital injections. The surplus is modeled by a regime-switching jump diffu...
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| Veröffentlicht in: | Automatica (Oxford) Jg. 49; H. 8; S. 2317 - 2329 |
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| Abstract | This work focuses on numerical methods for finding optimal investment, dividend payment, and capital injection policies to maximize the present value of the difference between the cumulative dividend payment and the possible capital injections. The surplus is modeled by a regime-switching jump diffusion process subject to both regular and singular controls. Using the dynamic programming principle, the value function is a solution of the coupled system of nonlinear integro-differential quasi-variational inequalities. In this paper, the state constraint of the impulsive control gives rise to a capital injection region with free boundary, which makes the problem even more difficult to analyze. Together with the regular control and regime-switching, the closed-form solutions are virtually impossible to obtain. We use Markov chain approximation techniques to construct a discrete-time controlled Markov chain to approximate the value function and optimal controls. Convergence of the approximation algorithms is proved. Examples are presented to illustrate the applicability of the numerical methods. |
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| AbstractList | This work focuses on numerical methods for finding optimal investment, dividend payment, and capital injection policies to maximize the present value of the difference between the cumulative dividend payment and the possible capital injections. The surplus is modeled by a regime-switching jump diffusion process subject to both regular and singular controls. Using the dynamic programming principle, the value function is a solution of the coupled system of nonlinear integro-differential quasi-variational inequalities. In this paper, the state constraint of the impulsive control gives rise to a capital injection region with free boundary, which makes the problem even more difficult to analyze. Together with the regular control and regime-switching, the closed-form solutions are virtually impossible to obtain. We use Markov chain approximation techniques to construct a discrete-time controlled Markov chain to approximate the value function and optimal controls. Convergence of the approximation algorithms is proved. Examples are presented to illustrate the applicability of the numerical methods. |
| Author | Jin, Zhuo Yang, Hailiang George Yin, G. |
| Author_xml | – sequence: 1 givenname: Zhuo surname: Jin fullname: Jin, Zhuo email: zjin@unimelb.edu.au organization: Centre for Actuarial Studies, Department of Economics, The University of Melbourne, VIC 3010, Australia – sequence: 2 givenname: Hailiang surname: Yang fullname: Yang, Hailiang email: hlyang@hkusua.hku.hk organization: Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong – sequence: 3 givenname: G. surname: George Yin fullname: George Yin, G. email: gyin@math.wayne.edu organization: Department of Mathematics, Wayne State University, Detroit, MI 48202, United States |
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| Keywords | Singular control Dividend policy Free boundary Markov chain approximation Investment strategy Stochastic control Capital injection Approximation algorithm Modeling Surplus Private equity Markov chain Variational inequality Diffusion process Jump process Dynamic programming Integrodifferential equation State constraint Dividend Time series Non linear system Exact solution Optimal control regime switching model Discrete time Investment |
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| SubjectTerms | Applied sciences Approximation Calculus of variations and optimal control Capital injection Control equipment Diffusion Dividend policy Exact sciences and technology Firm modelling Free boundary Inference from stochastic processes; time series analysis Investment strategy Markov chain approximation Markov chains Mathematical analysis Mathematical models Mathematical programming Mathematics Numerical analysis Operational research and scientific management Operational research. Management science Optimization Probability and statistics Sciences and techniques of general use Singular control Statistics Stochastic control |
| Title | Numerical methods for optimal dividend payment and investment strategies of regime-switching jump diffusion models with capital injections |
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