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Optimal investment and reinsurance under exponential forward preferences

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  • Katia Colaneri
  • Alessandra Cretarola
  • Benedetta Salterini

Abstract

We study the optimal investment and proportional reinsurance problem of an insurance company, whose investment preferences are described via a forward dynamic utility of exponential type in a stochastic factor model allowing for a possible dependence between the financial and insurance markets. Specifically, we assume that the asset price process dynamics and the claim arrival intensity are both affected by a common stochastic process and we account for a possible environmental contagion effect through the non-zero correlation parameter between the underlying Brownian motions driving the asset price process and the stochastic factor dynamics. By stochastic control techniques, we construct a forward dynamic exponential utility, and we characterize the optimal investment and reinsurance strategy. Moreover, we investigate in detail the zero-volatility case and provide a comparison analysis with classical results in an analogous setting under backward utility preferences. We also discuss an extension of the conditional certainty equivalent. Finally, we perform a numerical analysis to highlight some features of the optimal strategy.

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  • Katia Colaneri & Alessandra Cretarola & Benedetta Salterini, 2022. "Optimal investment and reinsurance under exponential forward preferences," Papers 2210.10425, arXiv.org.
    • Handle: RePEc:arx:papers:2210.10425
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    References listed on IDEAS

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    1. Thaleia Zariphopoulou, 2001. "A solution approach to valuation with unhedgeable risks," Finance and Stochastics, Springer, vol. 5(1), pages 61-82.
    2. M. Musiela & T. Zariphopoulou, 2009. "Portfolio choice under dynamic investment performance criteria," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 161-170.
    3. Gu, Ailing & Viens, Frederi G. & Yi, Bo, 2017. "Optimal reinsurance and investment strategies for insurers with mispricing and model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 235-249.
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    Cited by:

    1. Kenneth Tsz Hin Ng & Wing Fung Chong, 2023. "Optimal Investment in Defined Contribution Pension Schemes with Forward Utility Preferences," Papers 2303.08462, arXiv.org, revised Sep 2023.

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