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Optimal investment, consumption and life insurance under mean-reverting returns: The complete market solution

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  • Pirvu, Traian A.
  • Zhang, Huayue

Abstract

This paper considers the problem of optimal investment, consumption and life insurance acquisition for a wage earner who has CRRA (constant relative risk aversion) preferences. The market model is complete, continuous, the uncertainty is driven by Brownian motion and the stock price has mean reverting drift. The problem is solved by dynamic programming approach and the HJB equation is shown to have closed form solution. Numerical experiments explore the impact market price of risk has on the optimal strategies.

Suggested Citation

  • Pirvu, Traian A. & Zhang, Huayue, 2012. "Optimal investment, consumption and life insurance under mean-reverting returns: The complete market solution," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 303-309.
    • Handle: RePEc:eee:insuma:v:51:y:2012:i:2:p:303-309
    DOI: 10.1016/j.insmatheco.2012.05.002
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    References listed on IDEAS

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    1. 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.
    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    3. Munk, Claus & Sørensen, Carsten, 2010. "Dynamic asset allocation with stochastic income and interest rates," Journal of Financial Economics, Elsevier, vol. 96(3), pages 433-462, June.
    4. I. Duarte & Diogo Pinheiro & Alberto A. Pinto & S. R. Pliska, 2011. "Optimal life insurance purchase, consumption and investment on a financial market with multi-dimensional diffusive terms," CEMAPRE Working Papers 1102, Centre for Applied Mathematics and Economics (CEMAPRE), School of Economics and Management (ISEG), Technical University of Lisbon.
    5. repec:dau:papers:123456789/11473 is not listed on IDEAS
    6. Wolfram Horneff & Raimond Maurer, 2009. "Mortality Contingent Claims: Impact of Capital Market, Income, and Interest Rate Risk," Working Papers wp222, University of Michigan, Michigan Retirement Research Center.
    7. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    8. Todor Stoilov (ed.), 2012. "Time Management," Books, IntechOpen, number 2056, January-J.
    9. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    10. 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:

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    8. Tianxiao Wang, 2012. "Risk minimizing of derivatives via dynamic g-expectation and related topics," Papers 1208.2068, arXiv.org.
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    10. Peng, Xingchun & Li, Baihui, 2023. "Optimal investment, consumption and life insurance purchase with learning about return predictability," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 70-95.
    11. Francesco Menoncin & Luca Regis, 2015. "Longevity assets and pre-retirement consumption/portfolio decisions," Working Papers 2/2015, IMT School for Advanced Studies Lucca, revised May 2015.
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    13. Kwak, Minsuk & Lim, Byung Hwa, 2014. "Optimal portfolio selection with life insurance under inflation risk," Journal of Banking & Finance, Elsevier, vol. 46(C), pages 59-71.
    14. 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.
    15. Wei, Jiaqin & Cheng, Xiang & Jin, Zhuo & Wang, Hao, 2020. "Optimal consumption–investment and life-insurance purchase strategy for couples with correlated lifetimes," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 244-256.
    16. Rui Jiao & Wei Liu & Yijun Hu, 2023. "The Optimal Consumption, Investment and Life Insurance for Wage Earners under Inside Information and Inflation," Mathematics, MDPI, vol. 11(15), pages 1-18, August.
    17. Chen, An & Hentschel, Felix & Klein, Jakob K., 2015. "A utility- and CPT-based comparison of life insurance contracts with guarantees," Journal of Banking & Finance, Elsevier, vol. 61(C), pages 327-339.
    18. Gaurav Khemka & Adam Butt, 2017. "Non-Parametric Integral Estimation Using Data Clustering in Stochastic dynamic Programming: An Introduction Using Lifetime Financial Modelling," Risks, MDPI, vol. 5(4), pages 1-17, October.
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    20. Bin Zou & Abel Cadenillas, 2014. "Explicit Solutions of Optimal Consumption, Investment and Insurance Problem with Regime Switching," Papers 1402.3562, arXiv.org, revised Jun 2014.
    21. Yao, Haixiang & Li, Danping & Wu, Huiling, 2022. "Dynamic trading with uncertain exit time and transaction costs in a general Markov market," International Review of Financial Analysis, Elsevier, vol. 84(C).

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