Special Session 146: 

Expected exponential utility maximization of insurers with a general diffusion factor model : The complete market case.

Hiroaki Hata
Shizuoka university
Co-Author(s):    Shuenn-Jyi Sheu(National Central University, Taiwan), and Li-Hsien Sun(National Central University, Taiwan)
In this talk, we consider the problem of optimal investment by an insurer. The insurer invests in a market consisting of a bank account and $m$ risky assets. The mean returns and volatilities of the risky assets depend nonlinearly on economic factors that are formulated as the solutions of general stochastic differential equations. The wealth of the insurer is described by a Cramer--Lundberg process, and the insurer preferences are exponential. Adapting a dynamic programming approach, we derive Hamilton--Jacobi--Bellman (HJB) equation. And, we prove the unique solvability of HJB equation. In addition, the optimal strategy is obtained using the coupled forward and backward stochastic differential equations. Finally, proving the verification theorem, we construct the optimal strategy.