Optimal investment and proportional reinsurance with risk constraint

J. Liu, Ka Fai Cedric Yiu, R.C. Loxton, K.L. Teo

Research output: Journal article publicationJournal articleAcademic researchpeer-review


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 stochastic optimal control problem. It is difficult to solve a constrained stochastic optimal control problem by using traditional 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 deterministic 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 demonstrate the effect of the risk constraint on the optimal strategy.
Original languageEnglish
Pages (from-to)437-447
Number of pages11
JournalJournal of mathematical finance
Issue number4
Publication statusPublished - Nov 2013


  • Proportional reinsurance
  • Martingale transform
  • Value-at-risk
  • Stochastic control
  • Deterministic optimal control


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