Optimal reinsurance-investment with loss aversion under rough Heston model

Abstract

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.

Keywords:

• Reinsurance-investment strategies
• Rough Heston model
• Approximate solutions
• Dual control
• Monte-Carlo methods

JEL Classification:

• C20
• C61
• G11

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was supported by the National Natural Science Foundation of China [grant number 12071373].