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Optimal financing and dividend distribution in a general diffusion model with regime switching

Part of: Hamilton-Jacobi theories, including dynamic programming Mathematical finance

Published online by Cambridge University Press:  10 June 2016

Jinxia Zhu  and
Hailiang Yang
Jinxia Zhu*
Affiliation:
The University of New South Wales
Hailiang Yang*
Affiliation:
The University of Hong Kong
*
* Postal address: School of Risk and Actuarial Studies, The University of New South Wales, Kensington Campus, NSW 2052, Australia. Email address: jinxia.zhu@unsw.edu.au
** Postal address: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong. Email address: hlyang@hku.hk
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Abstract

We study the optimal financing and dividend distribution problem with restricted dividend rates in a diffusion type surplus model, where the drift and volatility coefficients are general functions of the level of surplus and the external environment regime. The environment regime is modeled by a Markov process. Both capital injection and dividend payments incur expenses. The objective is to maximize the expectation of the total discounted dividends minus the total cost of the capital injection. We prove that it is optimal to inject capital only when the surplus tends to fall below 0 and to pay out dividends at the maximal rate when the surplus is at or above the threshold, dependent on the environment regime.

Keywords

Dividendgeneral diffusionoptimizationoptimal financingregime-switching

MSC classification

Primary: 49L20: Dynamic programming method
Secondary: 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 2 , June 2016 , pp. 406 - 422
Copyright
Copyright © Applied Probability Trust 2016 

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