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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Vydáno v:Automatica (Oxford) Ročník 49; číslo 8; s. 2317 - 2329
Hlavní autoři: Jin, Zhuo, Yang, Hailiang, George Yin, G.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Kidlington Elsevier Ltd 01.08.2013
Elsevier
Témata:
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
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
ISSN:0005-1098, 1873-2836
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
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content type line 23
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2013.04.043