Optimal reinsurance-investment with loss aversion under rough Heston model
研究了保险公司在粗糙赫斯顿模型下，通过购买比例再保险和投资无风险与风险资产来最大化S型效用的问题，采用半鞅逼近和蒙特卡洛方法求解最优策略。
The paper investigates optimal reinsurance-investment strategies with the assumption that the insurers can purchase proportional reinsurance contracts and invest their wealth in a financial market consisting of one risk-free asset and one risky asset whose price process obeys the rough Heston model. The problem is formulated as a utility maximization problem with a minimum guarantee under an S-shaped utility. Since the rough Heston model is non-Markovian and non-semimartingale, the utility maximization problem cannot be solved by the classical dynamical programming principle and related approaches. This paper uses semi-martingale approximation techniques to approximate the utility maximization problem and proves the rates of convergence for the optimal strategies. The approximate problem is a kind of classical stochastic control problem under multi-factor stochastic volatility models. As the approximate control problem still cannot be solved analytically, a dual-control Monte-Carlo method is developed to solve it. Numerical examples and implementations are provided.