Open Access JMF Optimal Investment and Proportional Reinsurance with Risk Constraint

Copyright © 2013 Jingzhen Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, we investigate the problem of maximizing the expected exponential utility for an insurer. In the problem setting, the insurer can invest his/her wealth into the market and he/she can also purchase the proportional reinsurance. To control the risk exposure, we impose a value-at-risk constraint on the portfolio, which results in a constrained sto-chastic optimal control problem. It is difficult to solve a constrained stochastic optimal control problem by using tradi-tional dynamic programming or Martingale approach. However, for the frequently used exponential utility function, we show that the problem can be simplified significantly using a decomposition approach. The problem is reduced to a de-terministic constrained optimal control problem, and then to a finite dimensional optimization problem. To show the effectiveness of the approach proposed, we consider both complete and incomplete markets; the latter arises when the number of risky assets are fewer than the dimension of uncertainty. We also conduct numerical experiments to demon-strate the effect of the risk constraint on the optimal strategy