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Random distribution kernels and three types of defaultable contingent payoffs

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  • Ye, Jinchun

Abstract

We introduce the random distribution kernel on a product probability space and obtain the representation results connecting the product and base probability spaces. Using the random variable with the random distribution kernel to model default/death time, we then consider three types of defaultable contingent payoffs. By allowing the survival conditioning time to be anytime before the start time of the payoffs, between the start time and end time, or after the end time of the payoffs, we provide the complete treatment of three types of defaultable contingent payoffs. As the application of the general results developed in this paper, we also provide the more general results for three types of defaultable contingent payoffs than the ones in the literature under the stochastic intensity framework.

Suggested Citation

  • Ye, Jinchun, 2019. "Random distribution kernels and three types of defaultable contingent payoffs," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 198-204.
    • Handle: RePEc:eee:insuma:v:85:y:2019:i:c:p:198-204
    DOI: 10.1016/j.insmatheco.2019.01.004
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    References listed on IDEAS

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    1. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
    2. Pliska, Stanley R. & Ye, Jinchun, 2007. "Optimal life insurance purchase and consumption/investment under uncertain lifetime," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1307-1319, May.
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    Cited by:

    1. Zaevski, Tsvetelin S. & Kounchev, Ognyan & Savov, Mladen, 2019. "Two frameworks for pricing defaultable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 309-319.
    2. Ye, Jinchun, 2019. "Stochastic utilities with subsistence and satiation: Optimal life insurance purchase, consumption and investment," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 193-212.

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    More about this item

    Keywords

    Random distribution kernel; Representation theorem; Stochastic intensity; Credit/mortality risk; Three types of defaultable contingent payoffs;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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