Elliott, RobertSiu, Tak Kuen2012-06-132012-06-132011Robert J. Elliott, Tak Kuen Siu, A BSDE approach to a risk-based optimal investment of an insurer, Automatica, Volume 47, Issue 2, February 2011, Pages 253-261.0005-1098http://hdl.handle.net/1880/48999Article deposited according to publisher policy posted on SHERPA/ROMEO, June 13, 2012.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.engBackward stochastic differential equationOptimal investmentInsurance companyConvex risk measureDiffusion approximationZero-sum stochastic differential gameExistence and uniqueness of optimal strategiesjournal article10.11575/PRISM/34054