Elliott, R.Siu, T.2012-02-012012-02-012011Automatica, 2011; 47(2):253-2610005-10981873-2836http://hdl.handle.net/2440/69332We 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. © 2010 Elsevier Ltd. All rights reserved.en© 2010 Elsevier Ltd. All rights reserved.Backward stochastic differential equationOptimal investmentInsurance companyConvex risk measureDiffusion approximationZero-sum stochastic differential gameExistence and uniqueness of optimal strategiesJournal article002011076510.1016/j.automatica.2010.10.0320002872641000012-s2.0-7875164772728707