A BSDE approach to a risk-based optimal investment of an insurer
| dc.contributor.author | Elliott, R. | |
| dc.contributor.author | Siu, T. | |
| dc.date.issued | 2011 | |
| dc.description.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. | |
| dc.description.statementofresponsibility | Robert J. Elliott and Tak Kuen Siu | |
| dc.description.uri | http://www.journals.elsevier.com/automatica/ | |
| dc.identifier.citation | Automatica, 2011; 47(2):253-261 | |
| dc.identifier.doi | 10.1016/j.automatica.2010.10.032 | |
| dc.identifier.issn | 0005-1098 | |
| dc.identifier.issn | 1873-2836 | |
| dc.identifier.uri | http://hdl.handle.net/2440/69332 | |
| dc.language.iso | en | |
| dc.publisher | Pergamon-Elsevier Science Ltd | |
| dc.relation.grant | http://purl.org/au-research/grants/arc/DP1096243 | |
| dc.rights | © 2010 Elsevier Ltd. All rights reserved. | |
| dc.source.uri | https://doi.org/10.1016/j.automatica.2010.10.032 | |
| dc.subject | Backward stochastic differential equation | |
| dc.subject | Optimal investment | |
| dc.subject | Insurance company | |
| dc.subject | Convex risk measure | |
| dc.subject | Diffusion approximation | |
| dc.subject | Zero-sum stochastic differential game | |
| dc.subject | Existence and uniqueness of optimal strategies | |
| dc.title | A BSDE approach to a risk-based optimal investment of an insurer | |
| dc.type | Journal article | |
| pubs.publication-status | Published |