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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, December.
    • 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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