2015/06/28 by Jinxia Zhu, Zhu, Jinxia, Hailiang Yang +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.OC #q-fin.PM
paper · pdf · doi:10.48550/arxiv.1506.08360
arxiv created 2015/06/28 · openalex publication_date 2015/06/28 · arxiv updated 2015/06/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 injections and dividend payments incur expenses. The objective is to maximize the expectation of the total discounted dividends minus the total cost of capital injections. We prove that it is optimal to inject capitals only when the surplus tends to fall below zero and to pay out dividends at the maximal rate when the surplus is at or above the threshold dependent on the environment regime.