Heston模型下基于期权投资的鲁棒最优控制

Robust optimal control for derivative-based investment under the Heston model

针对Heston随机波动率模型下的鲁棒最优投资问题,构建了带期权投资的资产负债管理模型.投资者的目标是最大化终端时刻净财富的幂效用,利用随机最优控制方法,分别获得了带期权投资以及无期权投资两种情形下鲁棒最优投资策略、最坏概率测度及值函数的解析表达式,通过数值模拟发现考虑模型的鲁棒性以及进行期权投资能够改进投资者的效用.

With regard to the robust optimal investment problem for an ambiguity-averse investor(AAI)with stochastic volatility,an asset-liability management model with derivative-based investment is constructed.The objective of investors is to maximize the power utility of net wealth at the end of time.The paper derives the explicit expressions for the robust optimal investment strategy,the worst-case scenario and the corresponding value function with and without derivative investment respectively by means of using stochastic optimal control method.The result of the numerical simulation shows that the established model and its algorithm are feasible and effective.Considering the robustness of the model and derivative trading the model can improve the utility of the investor.