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A BSDE approach to a risk-based optimal investment of an insurer

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Author
Elliott, Robert
Siu, Tak Kuen
Accessioned
2012-06-13T21:42:22Z
Available
2012-06-13T21:42:22Z
Issued
2011
Other
Insurance company
Convex risk measure
Diffusion approximation
Zero-sum stochastic differential game
Existence and uniqueness of optimal strategies
Subject
Backward stochastic differential equation
Optimal investment
Type
journal article
Metadata
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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.
Refereed
Yes
Article deposited according to publisher policy posted on SHERPA/ROMEO, June 13, 2012.
 
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.
Corporate
University of Calgary
Faculty
Haskayne School of Business
Hasversion
Post-print
Url
http://www.journals.elsevier.com/automatica/
Publisher
Elsevier
Doi
http://dx.doi.org/10.11575/PRISM/34054
Uri
http://hdl.handle.net/1880/48999
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  • Haskayne School of Business Research & Publications

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