Optimal investment and proportional reinsurance with risk constraint
In this paper, we investigate the problem of maximizing the expected exponential utility for an insurer. In the problem setting, the insurer can invest his/her wealth into the market and he/she can also purchase the proportional reinsurance. To control the risk exposure, we impose a value-at-risk co...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
Scientific Research Publishing
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/33258 |
| _version_ | 1848753895274184704 |
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| author | Liu, J. Yiu, K. Loxton, Ryan Teo, Kok Lay |
| author_facet | Liu, J. Yiu, K. Loxton, Ryan Teo, Kok Lay |
| author_sort | Liu, J. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we investigate the problem of maximizing the expected exponential utility for an insurer. In the problem setting, the insurer can invest his/her wealth into the market and he/she can also purchase the proportional reinsurance. To control the risk exposure, we impose a value-at-risk constraint on the portfolio, which results in a constrained stochastic optimal control problem. It is difficult to solve a constrained stochastic optimal control problem by using traditional dynamic programming or Martingale approach. However, for the frequently used exponential utility function, we show that the problem can be simplified significantly using a decomposition approach. The problem is reduced to a deterministic constrained optimal control problem, and then to a finite dimensional optimization problem. To show the effectiveness of the approach proposed, we consider both complete and incomplete markets; the latter arises when the number of risky assets are fewer than the dimension of uncertainty. We also conduct numerical experiments to demonstrate the effect of the risk constraint on the optimal strategy. |
| first_indexed | 2025-11-14T08:31:47Z |
| format | Journal Article |
| id | curtin-20.500.11937-33258 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:31:47Z |
| publishDate | 2013 |
| publisher | Scientific Research Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-332582017-09-13T15:30:25Z Optimal investment and proportional reinsurance with risk constraint Liu, J. Yiu, K. Loxton, Ryan Teo, Kok Lay deterministic optimal control proportional reinsurance value-at-risk stochastic control martingale transform In this paper, we investigate the problem of maximizing the expected exponential utility for an insurer. In the problem setting, the insurer can invest his/her wealth into the market and he/she can also purchase the proportional reinsurance. To control the risk exposure, we impose a value-at-risk constraint on the portfolio, which results in a constrained stochastic optimal control problem. It is difficult to solve a constrained stochastic optimal control problem by using traditional dynamic programming or Martingale approach. However, for the frequently used exponential utility function, we show that the problem can be simplified significantly using a decomposition approach. The problem is reduced to a deterministic constrained optimal control problem, and then to a finite dimensional optimization problem. To show the effectiveness of the approach proposed, we consider both complete and incomplete markets; the latter arises when the number of risky assets are fewer than the dimension of uncertainty. We also conduct numerical experiments to demonstrate the effect of the risk constraint on the optimal strategy. 2013 Journal Article http://hdl.handle.net/20.500.11937/33258 10.4236/jmf.2013.34046 Scientific Research Publishing fulltext |
| spellingShingle | deterministic optimal control proportional reinsurance value-at-risk stochastic control martingale transform Liu, J. Yiu, K. Loxton, Ryan Teo, Kok Lay Optimal investment and proportional reinsurance with risk constraint |
| title | Optimal investment and proportional reinsurance with risk constraint |
| title_full | Optimal investment and proportional reinsurance with risk constraint |
| title_fullStr | Optimal investment and proportional reinsurance with risk constraint |
| title_full_unstemmed | Optimal investment and proportional reinsurance with risk constraint |
| title_short | Optimal investment and proportional reinsurance with risk constraint |
| title_sort | optimal investment and proportional reinsurance with risk constraint |
| topic | deterministic optimal control proportional reinsurance value-at-risk stochastic control martingale transform |
| url | http://hdl.handle.net/20.500.11937/33258 |