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Optimal Consumption and Insurance: A Continuous-time Markov Chain Approach

Author

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  • Kraft, Holger
  • Steffensen, Mogens

Abstract

Personal financial decision making plays an important role in modern finance. Decision problems about consumption and insurance are in this article modelled in a continuous-time multi-state Markovian framework. The optimal solution is derived and studied. The model, the problem, and its solution are exemplified by two special cases: In one model the individual takes optimal positions against the risk of dying; in another model the individual takes optimal positions against the risk of losing income as a consequence of disability or unemployment.

Suggested Citation

  • Kraft, Holger & Steffensen, Mogens, 2008. "Optimal Consumption and Insurance: A Continuous-time Markov Chain Approach," ASTIN Bulletin, Cambridge University Press, vol. 38(1), pages 231-257, May.
    • Handle: RePEc:cup:astinb:v:38:y:2008:i:01:p:231-257_01
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    Citations

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    Cited by:

    1. Christoph Hambel & Holger Kraft & Lorenz S. Schendel & Mogens Steffensen, 2017. "Life Insurance Demand Under Health Shock Risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(4), pages 1171-1202, December.
    2. Konicz, Agnieszka Karolina & Mulvey, John M., 2015. "Optimal savings management for individuals with defined contribution pension plans," European Journal of Operational Research, Elsevier, vol. 243(1), pages 233-247.
    3. Erhan Bayraktar & Virginia Young, 2013. "Life Insurance Purchasing to Maximize Utility of Household Consumption," North American Actuarial Journal, Taylor & Francis Journals, vol. 17(2), pages 114-135.
    4. 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.
    5. Bruhn, Kenneth & Steffensen, Mogens, 2011. "Household consumption, investment and life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 315-325, May.
    6. Loretta Mastroeni & Maurizio Naldi & Pierluigi Vellucci, 2019. "Personal Finance Decisions with Untruthful Advisors: an Agent-Based Model," Papers 1909.06759, arXiv.org.
    7. Jarner, Søren Fiig & Kronborg, Morten Tolver, 2016. "Entrance times of random walks: With applications to pension fund modeling," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 1-20.
    8. Jensen, N.R. & Steffensen, M., 2015. "Personal finance and life insurance under separation of risk aversion and elasticity of substitution," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 28-41.
    9. Schendel, Lorenz S., 2014. "Consumption-investment problems with stochastic mortality risk," SAFE Working Paper Series 43, Leibniz Institute for Financial Research SAFE.
    10. Loretta Mastroeni & Maurizio Naldi & Pierluigi Vellucci, 2023. "Personal Finance Decisions with Untruthful Advisors: An Agent-Based Model," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1477-1522, April.
    11. Holger Kraft & Claus Munk, 2011. "Optimal Housing, Consumption, and Investment Decisions over the Life Cycle," Management Science, INFORMS, vol. 57(6), pages 1025-1041, June.
    12. Debbie Kusch Falden & Anna Kamille Nyegaard, 2021. "Retrospective Reserves and Bonus with Policyholder Behavior," Risks, MDPI, vol. 9(1), pages 1-28, January.
    13. Kraft, Holger & Schendel, Lorenz S. & Steffensen, Mogens, 2014. "Life insurance demand under health shock risk," SAFE Working Paper Series 40, Leibniz Institute for Financial Research SAFE.
    14. Hambel, Christoph, 2020. "Health shock risk, critical illness insurance, and housing services," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 111-128.
    15. Zhang, Jinhui & Purcal, Sachi & Wei, Jiaqin, 2021. "Optimal life insurance and annuity demand under hyperbolic discounting when bequests are luxury goods," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 80-90.

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