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

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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. Loretta Mastroeni & Maurizio Naldi & Pierluigi Vellucci, 2019. "Personal Finance Decisions with Untruthful Advisors: an Agent-Based Model," Papers 1909.06759, arXiv.org.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Schendel, Lorenz S., 2014. "Consumption-investment problems with stochastic mortality risk," SAFE Working Paper Series 43, Leibniz Institute for Financial Research SAFE.
    7. 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.
    8. 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.
    9. 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.
    10. Debbie Kusch Falden & Anna Kamille Nyegaard, 2021. "Retrospective Reserves and Bonus with Policyholder Behavior," Risks, MDPI, vol. 9(1), pages 1-28, January.
    11. 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.
    12. 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.
    13. Bruhn, Kenneth & Steffensen, Mogens, 2011. "Household consumption, investment and life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 315-325, May.
    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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