Ken Siu Seminar
- Topic: A BSDE Approach to a Risk-Based Optimal Investment of an Insurer
- Speaker: Associate Professor Ken Siu, Department of Applied Finance and Actuarial Studies, Macquarie University
- When: 12th October, 2011, (Wed)
We discuss a backward stochastic differential equation, (BSDE), approach to a risk-based, optimal investment problem of an insurer. A simplified continuous-time economy with two investment vehicles, namely, a fixed interest security and a share, is considered. The insurer's risk process is modelled by a diffusion approximation to a compound Poisson risk process. The goal of the insurer is to select an optimal portfolio so as to minimize the risk described by a convex risk measure of his/her terminal wealth.
The optimal investment problem is then formulated as a zero-sum stochastic differential game between the insurer and the market. The BSDE approach is used to solve the game problem. It leads to a simple and natural approach for the existence and uniqueness of an optimal strategy of the game problem without Markov assumptions. Closed-form solutions to the optimal strategies of the insurer and the market are obtained in some particular cases.
(This is joint work with Professor Robert J. Elliott).