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No-Good-Deal, Local Mean-Variance and Ambiguity Risk Pricing and Hedging for an Insurance Payment Process

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  • Delong, Å ukasz

Abstract

We study pricing and hedging for an insurance payment process. We investigate a Black-Scholes financial model with stochastic coefficients and a payment process with death, survival and annuity claims driven by a point process with a stochastic intensity. The dependence of the claims and the intensity on the financial market and on an additional background noise (correlated index, longevity risk) is allowed. We establish a general modeling framework for no-good-deal, local mean-variance and ambiguity risk pricing and hedging. We show that these three valuation approaches are equivalent under appropriate formulations. We characterize the price and the hedging strategy as a solution to a backward stochastic differential equation. The results could be applied to pricing and hedging of variable annuities, surrender options under an irrational lapse behavior and mortality derivatives.

Suggested Citation

  • Delong, Å ukasz, 2012. "No-Good-Deal, Local Mean-Variance and Ambiguity Risk Pricing and Hedging for an Insurance Payment Process," ASTIN Bulletin, Cambridge University Press, vol. 42(1), pages 203-232, May.
    • Handle: RePEc:cup:astinb:v:42:y:2012:i:01:p:203-232_00
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    Cited by:

    1. Christophette Blanchet-Scalliet & Diana Dorobantu & Yahia Salhi, 2016. "A Model-Point Approach to Indifference Pricing of Life Insurance Portfolios with Dependent Lives," Working Papers hal-01258645, HAL.
    2. Dirk Becherer & Klebert Kentia, 2017. "Hedging under generalized good-deal bounds and model uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 171-214, August.
    3. Christophette Blanchet-Scalliet & Diana Dorobantu & Yahia Salhi, 2019. "A Model-Point Approach to Indifference Pricing of Life Insurance Portfolios with Dependent Lives," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 423-448, June.
    4. Claudia Ceci & Katia Colaneri & Alessandra Cretarola, 2018. "Indifference pricing of pure endowments via BSDEs under partial information," Papers 1804.00223, arXiv.org, revised Jul 2020.
    5. Christophette Blanchet-Scalliet & Diana Dorobantu & Yahia Salhi, 2019. "A Model-Point Approach to Indifference Pricing of Life Insurance Portfolios with Dependent Lives," Post-Print hal-01258645, HAL.
    6. Dirk Becherer & Klebert Kentia, 2016. "Hedging under generalized good-deal bounds and model uncertainty," Papers 1607.04488, arXiv.org, revised Apr 2017.

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