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Optimal investment and reinsurance under exponential forward preferences

Author

Listed:
  • Katia Colaneri

    (University of Rome Tor Vergata)

  • Alessandra Cretarola

    (University of Perugia)

  • Benedetta Salterini

    (University of Firenze)

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 dependence between the financial and insurance markets. Specifically, we assume that the asset price process dynamics and the claim arrival intensity are 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. 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 the indifference pricing problem for the portfolio of claims. Finally, we perform a numerical analysis to highlight some features of the optimal strategy.

Suggested Citation

  • Katia Colaneri & Alessandra Cretarola & Benedetta Salterini, 2025. "Optimal investment and reinsurance under exponential forward preferences," Mathematics and Financial Economics, Springer, volume 19, number 1, September.
    • Handle: RePEc:spr:mathfi:v:19:y:2025:i:1:d:10.1007_s11579-024-00372-0
    DOI: 10.1007/s11579-024-00372-0
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    References listed on IDEAS

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    1. Katia Colaneri & Alessandra Cretarola & Benedetta Salterini, 2021. "Optimal Investment and Proportional Reinsurance in a Regime-Switching Market Model under Forward Preferences," Mathematics, MDPI, vol. 9(14), pages 1-27, July.
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    7. Katia Colaneri & Alessandra Cretarola & Benedetta Salterini, 2021. "Optimal investment and proportional reinsurance in a regime-switching market model under forward preferences," Papers 2106.13888, arXiv.org.
    8. Colaneri, Katia & Frey, Rüdiger, 2021. "Classical solutions of the backward PIDE for Markov modulated marked point processes and applications to CAT bonds," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 498-507.
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    21. Fujin Zhou & Thijs Endendijk & W.J. Wouter Botzen, 2023. "A Review of the Financial Sector Impacts of Risks Associated with Climate Change," Annual Review of Resource Economics, Annual Reviews, vol. 15(1), pages 233-256, October.
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