Optimal investment and proportional reinsurance with risk constraint
MetadataShow full item record
This article is published under the Open Access publishing model and distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0/. Please refer to the licence to obtain terms for any further reuse or distribution of this work.
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.
Showing items related by title, author, creator and subject.
Li, Bin (2011)In this thesis, we consider several types of optimal control problems with constraints on the state and control variables. These problems have many engineering applications. Our aim is to develop efficient numerical methods ...
Loxton, Ryan Christopher (2010)In this thesis, we develop numerical methods for solving five nonstandard optimal control problems. The main idea of each method is to reformulate the optimal control problem as, or approximate it by, a nonlinear programming ...
Chai, Qinqin (2013)In this thesis, we develop new computational methods for three classes of dynamic optimization problems: (i) A parameter identification problem for a general nonlinear time-delay system; (ii) an optimal control problem ...