Optimal investment and risk control policies for an insurer in an incomplete market. (English) Zbl 1426.91238
Summary: In this paper, we apply the martingale approach to investigate the optimal investment and risk control problem for an insurer in an incomplete market. The claim risk of per policy is characterized by a compound Poisson process with drift, and the insurer can be invested in multiple risky assets whose price processes are described by the geometric Brownian motions model. By ‘complete’ the incomplete market, closed-form solutions to the problems of mean-variance criterion and expected exponential utility maximization are obtained. Moreover, numerical simulations are presented to illustrate the results with the basic parameters.
MSC:
| 91G05 | Actuarial mathematics |
| 60K30 | Applications of queueing theory (congestion, allocation, storage, traffic, etc.) |
| 60G44 | Martingales with continuous parameter |
| 91B16 | Utility theory |
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