带扰动的随机保费模型的渐近最优投资

本文研究了一类具有随机投资回报的随机保费模型的最小破产概率的渐近性质.在假定常值投资策略的情形下,通过最小化调节系数,我们得到了与此调节系数相对应的最优的常值投资策略.最后我们证明当初始盈余趋向于无穷的时候,最优的投资策略趋向于这个常值策略.

Asymptotically Optimal Investment for Risk Model with Random Income and Diffusions

In this paper, an insurer with perturbed classical risk process and random premium income has the possibility of investment into a risky market. The price process of the risky market is assumed to follow a geometric Brownian motion. The aim of this paper is to obtain the asymptotical behavior of the ruin probability under the optimal strategy in the small claims. The constant (denoted by A*) maximizing the Lundburg exponent is derived. It turns out that the optimal investment level convergence to A* when the initial surplus tends to infinity. That is to say, the constant we found is the asymptotically optimal strategy.