常利率风险模型下T-A目标函数的最大化

Maximization of T-A Objective Function for the Risk Model with Constant Interest Force

本文研究了带常利率扩散风险模型,考虑了下面的目标函数V(x,L)=E(integral from n=0 toτe^(-βt)dL_t+integral from n=0 toτe^(-βt)∧dt|R_0~L=x),这里常数∧≥0.我们称上面的表达式为T-A(Thonhauser and Albrecher)目标函数.对于常利率下的扩散模型,通过随机控制理论(HJB方程),T-A目标函数的最大化问题得以解决:对于有界分红率,最优策略是门槛策略;对于无界分红率,最优策略是边界策略.

In this paper,we study the diffusion risk model with constant interest force, and consider the following objective function where constant A≥0.We may call the above expression T-A（Thonhauser and Albrecher） objective function.For the diffusion risk model with constant interest force, maximization of T-A objective function is solved by stochastic control theory（HJB equations）：For bounded dividend intensity,optimal strategy is a threshold strategy; for unbounded dividend intensity,optimal strategy is a barrier strategy.