Optimal dividend policy when cash reserves follow a jump-diffusion process under Markov-regime switching. (English) Zbl 1325.93058

Jiang, Zhengjun

J. Appl. Probab. 52, No. 1, 209-223 (2015).

Summary: In this paper we study the optimal dividend payments for a company of limited liability whose cash reserves in the absence of dividends follow a Markov-modulated jump-diffusion process with positive drifts and negative exponential jumps, where parameters and discount rates are modulated by a finite-state irreducible Markov chain. The main aim is to maximize the expected cumulative discounted dividend payments until bankruptcy time when cash reserves are nonpositive for the first time. We extend the results of Z. Jiang and M. Pistorius [Finance Stoch. 16, No. 3, 449–476 (2012; Zbl 1252.93135)] to our setup by proving that it is optimal to adopt a modulated barrier strategy at certain positive regime-dependent levels and that the value function can be explicitly characterized as the fixed point of a contraction.

MSC:

93E20	Optimal stochastic control
91B70	Stochastic models in economics
60H30	Applications of stochastic analysis (to PDEs, etc.)
91G50	Corporate finance (dividends, real options, etc.)

Keywords:

optimal dividend policy; Markov chain; regime switching; jump-diffusion process; stochastic control

Citations:

Zbl 1252.93135