# Lukasz Delong: Optimal investment for insurance company with exponential utility and wealth-dependent risk aversion coefficient

**Time: **
Mon 2022-10-17 15.15 - 16.15

**Location: **
Room 3721, Lindstedtsvägen 25

**Participating: **
Lukasz Delong (Warsaw School of Economics)

### Abstract

We investigate an exponential utility maximization problem for an insurer who faces a stream of non-hedgeable claims. The insurer’s risk aversion coefficient changes in time and depends on the current insurer’s net asset value (the excess of assets over liabilities). We use the notion of an equilibrium strategy and derive the HJB equation for our time-inconsistent optimization problem. We assume that the insurer’s risk aversion coefficient consists of a constant risk aversion and a small amount of a wealth-dependent risk aversion. Using perturbation theory, the equilibrium value function, which solves the HJB equation, is expanded on the parameter controlling the degree of risk aversion depending on wealth. We propose the first-order approximations to the equilibrium value function and the equilibrium investment strategy and prove the asymptotic results.