跳扩散模型下基金平衡管理的最优脉冲控制

在基金市值波动服从跳扩散过程, 基金持有的罚金成本为当前基金水平的二次函数及存在交易费的假设下研究了无穷时域的基金平衡管理的最小成本模型. 利用随机最优脉冲控制的拟变分不等式理论建立了判定定理,得到了最优脉冲控制策略的存在性, 同时通过构造方法给出了解的数学结构形式.

Optimal Impulse Control for Cash Balance Management in Jump-Diffusion Model

This paper is concerned with studying a problem that minimizes the total expected discounted cost over an infinite horizon for a cash management, where the cash fund follows jump-diffusion processes, holding-costs are assumed to be a general quadratic function of the cash level and there exist fixed and proportional transaction costs. Thanks to the variational inequality method in stochastic impulse control theory, we obtain the verification theorem, prove that the optimal control exists, and also gain its mathematical structures.