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https://hdl.handle.net/2440/69332
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Type: | Journal article |
Title: | A BSDE approach to a risk-based optimal investment of an insurer |
Author: | Elliott, R. Siu, T. |
Citation: | Automatica, 2011; 47(2):253-261 |
Publisher: | Pergamon-Elsevier Science Ltd |
Issue Date: | 2011 |
ISSN: | 0005-1098 1873-2836 |
Statement of Responsibility: | Robert J. Elliott and Tak Kuen Siu |
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. |
Keywords: | Backward stochastic differential equation Optimal investment Insurance company Convex risk measure Diffusion approximation Zero-sum stochastic differential game Existence and uniqueness of optimal strategies |
Rights: | © 2010 Elsevier Ltd. All rights reserved. |
DOI: | 10.1016/j.automatica.2010.10.032 |
Grant ID: | http://purl.org/au-research/grants/arc/DP1096243 |
Description (link): | http://www.journals.elsevier.com/automatica/ |
Published version: | http://dx.doi.org/10.1016/j.automatica.2010.10.032 |
Appears in Collections: | Aurora harvest 5 Mathematical Sciences publications |
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