A BSDE approach to a risk-based optimal investment of an insurer
Date
2011
Authors
Elliott, R.
Siu, T.
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Journal article
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Automatica, 2011; 47(2):253-261
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Robert J. Elliott and Tak Kuen Siu
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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. © 2010 Elsevier Ltd. All rights reserved.
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© 2010 Elsevier Ltd. All rights reserved.