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On optimal investment in a reinsurance context with a point process market model

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  • Edoli, Enrico
  • Runggaldier, Wolfgang J.

Abstract

We study an insurance model where the risk can be controlled by reinsurance and investment in the financial market. We consider a finite planning horizon where the timing of the events, namely the arrivals of a claim and the change of the price of the underlying asset(s), corresponds to a Poisson point process. The objective is the maximization of the expected total utility and this leads to a nonstandard stochastic control problem with a possibly unbounded number of discrete random time points over the given finite planning horizon. Exploiting the contraction property of an appropriate dynamic programming operator, we obtain a value-iteration type algorithm to compute the optimal value and strategy and derive its speed of convergence. Following Schäl (2004) we consider also the specific case of exponential utility functions whereby negative values of the risk process are penalized, thus combining features of ruin minimization and utility maximization. For this case we are able to derive an explicit solution. Results of numerical computations are also reported.

Suggested Citation

  • Edoli, Enrico & Runggaldier, Wolfgang J., 2010. "On optimal investment in a reinsurance context with a point process market model," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 315-326, December.
    • Handle: RePEc:eee:insuma:v:47:y:2010:i:3:p:315-326
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    References listed on IDEAS

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    Cited by:

    1. Brandejsky, Adrien & de Saporta, Benoîte & Dufour, François, 2013. "Optimal stopping for partially observed piecewise-deterministic Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3201-3238.
    2. Zhou, Jieming & Yang, Xiangqun & Guo, Junyi, 2017. "Portfolio selection and risk control for an insurer in the Lévy market under mean–variance criterion," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 139-149.

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