A BSDE approach to a risk-based optimal investment of an insurer
Date
2011
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
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.
Description
Article deposited according to publisher policy posted on SHERPA/ROMEO, June 13, 2012.
Keywords
Backward stochastic differential equation, Optimal investment
Citation
Robert 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.