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Drawdown insurance contracts for the Lévy-type model with the phase-type jump distribution and general reward function

Author

Listed:
  • Zbigniew Palmowski

    (Politechnika Wrocławska, Wydział Matematyki)

  • Joanna Tumilewicz

    (Uniwersytet Wrocławski, Wydział Matematyki i Informatyki)

Abstract

In this paper, we consider an insurance contract which insure against a fall of some pre-specified level below an asset’s maximal value. This situation may cause huge losses to investors and it gives a reason to create an insurance against such a situation. We model a risky asset by the geometric Browanian motion with jumps having the phase-type distribution. We define the drawdown proces as a difference between the supremum of underlying process and its current value. For this model, we construct insturance against a huge drawdown. In this contract, an insurance company commits to pay reward at a drawdown epoch. In return, an investor pays continuously a consant premium up to the drawdown moment. This work is based on the paper of Palmowski and Tumilewicz18, in which the authors presented a mathematical model for some insurance contracts against the drawdown for spectrally negative Lévy processes. Here, we focus on numerical analysis of one of such contracts when jumps are of the phase-type.

Suggested Citation

  • Zbigniew Palmowski & Joanna Tumilewicz, 2018. "Drawdown insurance contracts for the Lévy-type model with the phase-type jump distribution and general reward function," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 51, pages 255-270.
    • Handle: RePEc:sgh:annals:i:51:y:2018:p:255-270
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    References listed on IDEAS

    as
    1. Palmowski, Zbigniew & Tumilewicz, Joanna, 2018. "Pricing insurance drawdown-type contracts with underlying Lévy assets," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 1-14.
    2. Libor Pospisil & Jan Vecer, 2010. "Portfolio sensitivity to changes in the maximum and the maximum drawdown," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 617-627.
    3. Peter Carr & Hongzhong Zhang & Olympia Hadjiliadis, 2011. "Maximum Drawdown Insurance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(08), pages 1195-1230.
    4. Zbigniew Palmowski & Joanna Tumilewicz, 2017. "Fair valuation of L\'evy-type drawdown-drawup contracts with general insured and penalty functions," Papers 1712.04418, arXiv.org, revised Feb 2018.
    5. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276, July.
    6. Zhang, Hongzhong & Leung, Tim & Hadjiliadis, Olympia, 2013. "Stochastic modeling and fair valuation of drawdown insurance," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 840-850.
    Full references (including those not matched with items on IDEAS)

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