Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/6965
Title: Optimal investment and proportional reinsurance with risk constraint
Authors: Liu, J
Yiu, KFC 
Loxton, RC
Teo, KL
Keywords: Proportional reinsurance
Martingale transform
Value-at-risk
Stochastic control
Deterministic optimal control
Issue Date: Nov-2013
Publisher: Scientific Research
Source: Journal of mathematical finance, Nov. 2013, v. 3, no. 4, p.437-447 How to cite?
Journal: Journal of mathematical finance 
Abstract: 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.
URI: http://hdl.handle.net/10397/6965
ISSN: 2162-2434 (print)
2162-2442 (online)
DOI: 10.4236/jmf.2013.34046
Rights: 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.
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