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Optimal reinsurance-investment with loss aversion under rough Heston model

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  • Jingtang Ma
  • Zhengyang Lu
  • Dengsheng Chen

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.

Suggested Citation

  • Jingtang Ma & Zhengyang Lu & Dengsheng Chen, 2023. "Optimal reinsurance-investment with loss aversion under rough Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 23(1), pages 95-109, January.
  • Handle: RePEc:taf:quantf:v:23:y:2023:i:1:p:95-109
    DOI: 10.1080/14697688.2022.2140308
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