Optimal investment with transaction costs and dividends for an insurer

¹ School of Statistics, East China Normal University, 500 Dongchuan Road, Shanghai 200241, P.R. China.
jnbi@sfs.ecnu.edu.cn
² Finance Department, School of Business, Renmin University of China, 59 Zhongguancun Street, Beijing 100872, P.R. China.
mengqb@yahoo.com.cn

Received: 14 April 2015
Accepted: 12 February 2016

Abstract

This paper investigates the optimal investment problems for an insurer whose reserve process is approximated by a diffusion model. The insurer is allowed to invest its wealth in the financial market consisting of one risk-free asset (bond) and one risky asset (stock). There are charges which equal to a fixed percentage of the amount transferred between the two assets. Under different criteria, we consider two optimization problems: one is maximizing the expected discounted utility of the dividends; the other is maximizing the insurer’s expected utility of the terminal wealth. We obtain that the optimal investment strategies are bang-bang strategies in both of the two problems. Numerical examples are given to illustrate our results.