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

Robert J. Elliott, Tak Kuen Siu

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)253-261
Number of pages9
JournalAutomatica
Volume47
Issue number2
DOIs
Publication statusPublished - Feb 2011

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