A BSDE approach to a risk-based optimal investment of an insurer

✍ Scribed by Robert J. Elliott; Tak Kuen Siu

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 357 KB
• Volume: 47
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/j.automatica.2010.10.032

✦ Synopsis

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 modeled 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.