Optimal investment under transaction costs for an insurer

Abstract

We deal with the problem of minimizing the probability of ruin of an insurer by optimal investment of parts of the surplus in the financial market, modeled by geometric Brownian motion. In a diffusion framework the classical solution to this problem is to hold a constant amount of money in stocks, which in practice means continuous adaption of the investment position. In this paper, we introduce both proportional and fixed transaction costs, which leads to a more realistic scenario. In mathematical terms, the problem is now of impulse control type. Its solution is characterized and calculated by iteration of associated optimal stopping problems. Finally some numerical examples illustrate the resulting optimal investment policy and its deviation from the optimal investment behaviour without transaction costs.