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Optimal investment-consumption and life insurance selection problem under inflation. A BSDE approach

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  • Calisto Guambe
  • Rodwell Kufakunesu

Abstract

We discuss an optimal investment, consumption and insurance problem of a wage earner under inflation. Assume a wage earner investing in a real money account and three asset prices, namely: a real zero coupon bond, the inflation-linked real money account and a risky share described by jump-diffusion processes. Using the theory of quadratic-exponential backward stochastic differential equation (BSDE) with jumps approach, we derive the optimal strategy for the two typical utilities (exponential and power) and the value function is characterized as a solution of BSDE with jumps. Finally, we derive the explicit solutions for the optimal investment in both cases of exponential and power utility functions for a diffusion case.

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  • Calisto Guambe & Rodwell Kufakunesu, 2017. "Optimal investment-consumption and life insurance selection problem under inflation. A BSDE approach," Papers 1711.01760, arXiv.org.
    • Handle: RePEc:arx:papers:1711.01760
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    References listed on IDEAS

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    1. Morlais, Marie-Amelie, 2010. "A new existence result for quadratic BSDEs with jumps with application to the utility maximization problem," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 1966-1995, September.
    2. Bernt Øksendal & Agnès Sulem, 2011. "Portfolio optimization under model uncertainty and BSDE games," Quantitative Finance, Taylor & Francis Journals, vol. 11(11), pages 1665-1674.
    3. Han, Nan-Wei & Hung, Mao-Wei, 2017. "Optimal consumption, portfolio, and life insurance policies under interest rate and inflation risks," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 54-67.
    4. Richard, Scott F., 1975. "Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model," Journal of Financial Economics, Elsevier, vol. 2(2), pages 187-203, June.
    5. Bernt Oksendal & Agnès Sulem, 2011. "Portfolio optimization under model uncertainty and BSDE games," Working Papers inria-00570532, HAL.
    6. 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.
    7. 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.
    8. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    9. Tiong, Serena, 2013. "Pricing inflation-linked variable annuities under stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 77-86.
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    Cited by:

    1. Calisto Guambe & Rodwell Kufakunesu & Gusti Van Zyl & Conrad Beyers, 2018. "Optimal asset allocation for a DC plan with partial information under inflation and mortality risks," Papers 1808.06337, arXiv.org, revised Aug 2018.

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