Sub-optimal investment for insurers. (English) Zbl 1511.91117
Summary: We consider the investment problem for a non-life insurance company seeking to minimize the ruin probability. Its reserve is described by a perturbed risk process possibly correlated with the financial market. Assuming exponential claim size, the Hamilton-Jacobi-Bellman equation reduces to a first order nonlinear ordinary differential equation, which seems hard to solve explicitly. We study the qualitative behavior of its solution and determine the Cramér-Lundberg approximation. Moreover, our approach enables to find very naturally that the optimal investment strategy is not constant. Then, we analyze how much the company looses by adopting sub-optimal constant (amount) investment strategies.
MSC:
| 91G05 | Actuarial mathematics |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
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