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Mean-variance hedging of unit linked life insurance contracts in a jump-diffusion model

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  • Frank Bosserhoff
  • Mitja Stadje

Abstract

We consider a time-consistent mean-variance portfolio selection problem of an insurer and allow for the incorporation of basis (mortality) risk. The optimal solution is identified with a Nash subgame perfect equilibrium. We characterize an optimal strategy as solution of a system of partial integro-differential equations (PIDEs), a so called extended Hamilton-Jacobi-Bellman (HJB) system. We prove that the equilibrium is necessarily a solution of the extended HJB system. Under certain conditions we obtain an explicit solution to the extended HJB system and provide the optimal trading strategies in closed-form. A simulation shows that the previously found strategies yield payoffs whose expectations and variances are robust regarding the distribution of jump sizes of the stock. The same phenomenon is observed when the variance is correctly estimated, but erroneously ascribed to the diffusion components solely. Further, we show that differences in the insurance horizon and the time to maturity of a longevity asset do not add to the variance of the terminal wealth.

Suggested Citation

  • Frank Bosserhoff & Mitja Stadje, 2019. "Mean-variance hedging of unit linked life insurance contracts in a jump-diffusion model," Papers 1908.05534, arXiv.org.
    • Handle: RePEc:arx:papers:1908.05534
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    References listed on IDEAS

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    1. Coughlan, Guy & Khalaf-Allah, Marwa & Ye, Yijing & Kumar, Sumit & Cairns, Andrew & Blake, David & Dowd, Kevin, 2011. "Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness," MPRA Paper 35743, University Library of Munich, Germany.
    2. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    3. LUCIANO, Elisa & VIGNA, Elena, 2008. "Mortality risk via affine stochastic intensities: calibration and empirical relevance," MPRA Paper 59627, University Library of Munich, Germany.
    4. Wang, J. & Forsyth, P.A., 2011. "Continuous time mean variance asset allocation: A time-consistent strategy," European Journal of Operational Research, Elsevier, vol. 209(2), pages 184-201, March.
    5. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    6. Christoph Czichowsky, 2013. "Time-consistent mean-variance portfolio selection in discrete and continuous time," Finance and Stochastics, Springer, vol. 17(2), pages 227-271, April.
    7. Guy Coughlan & Marwa Khalaf-Allah & Yijing Ye & Sumit Kumar & Andrew Cairns & David Blake & Kevin Dowd, 2011. "Longevity Hedging 101," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 150-176.
    8. Johnny Li & Mary Hardy, 2011. "Measuring Basis Risk in Longevity Hedges," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 177-200.
    9. Kromer, E. & Overbeck, L. & Röder, J.A.L., 2015. "Feynman–Kac for functional jump diffusions with an application to Credit Value Adjustment," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 120-129.
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