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A note on optimal investment–consumption–insurance in a Lévy market

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  • Guambe, Calisto
  • Kufakunesu, Rodwell

Abstract

In Shen and Wei (2014) an optimal investment, consumption and life insurance purchase problem for a wage earner with Brownian information has been investigated. This paper discusses the same problem but extend their results to a geometric Itô–Lévy jump process. Our modelling framework is very general as it allows random parameters which are unbounded and involves some jumps. It also covers parameters which are both Markovian and non-Markovian functionals. Unlike in Shen and Wei (2014) who considered a diffusion framework, ours solves the problem using a novel approach, which combines the Hamilton–Jacobi–Bellman (HJB) and a backward stochastic differential equation (BSDE) in a Lévy market setup. We illustrate our results by two examples.

Suggested Citation

  • Guambe, Calisto & Kufakunesu, Rodwell, 2015. "A note on optimal investment–consumption–insurance in a Lévy market," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 30-36.
    • Handle: RePEc:eee:insuma:v:65:y:2015:i:c:p:30-36
    DOI: 10.1016/j.insmatheco.2015.07.008
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    References listed on IDEAS

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    Cited by:

    1. Wang, Tao & Chen, Zhiping, 2024. "Optimal portfolio and insurance strategy with biometric risks, habit formation and smooth ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 118(C), pages 195-222.
    2. Rodwell Kufakunesu & Calisto Guambe, 2018. "On the optimal investment-consumption and life insurance selection problem with an external stochastic factor," Papers 1808.04608, arXiv.org.
    3. de Kort, J. & Vellekoop, M.H., 2017. "Existence of optimal consumption strategies in markets with longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 107-121.
    4. Calisto Guambe & Rodwell Kufakunesu, 2017. "Optimal investment-consumption and life insurance selection problem under inflation. A BSDE approach," Papers 1711.01760, arXiv.org.
    5. Delong, Łukasz & Chen, An, 2016. "Asset allocation, sustainable withdrawal, longevity risk and non-exponential discounting," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 342-352.

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