A dividend optimization problem with constraint of survival probability in a Markovian environment model

Abstract

In this paper, the optimal dividend problem in a discrete-time risk model with interest is discussed. Assume that the premium received per unit time is a positive real-valued random variable, and the sequence of premiums is a Markov chain owing to the environmental effects. In arbitrary unit time whether a claim occurs or not is related to the premium received in the corresponding period. Under the constraint of a given survival probability, the optimal control strategy for dividends paid periodically to the shareholders is considered. We provide some properties and an algorithm for the optimal control strategy by structuring a non-linear operator and applying the fixed point theorem. Numerical examples are presented to illustrate the algorithm.

Keywords:

• Optimal control strategy
• periodic dividends
• survival probability
• non-linear operator

MATHEMATICS SUBJECT CLASSIFICATION:

• (2010) 60G51
• 93E20

Additional information

Funding

Supported by Hunan Provincial Natural Science Foundation of China (No. 2019JJ40278), Hu Xiang Gao Ceng Ci Ren Cai Ju Jiao Gong Cheng-Chuang Xin Ren Cai (No. 2019RS1057), and the Natural Sciences Foundations of China (Nos. 61272294, 11371301).