Skip to main content
SpringerLink
Log in

Household utility maximization with life insurance: a CES utility case

  • Original Paper
  • Published:
Japan Journal of Industrial and Applied Mathematics Aims and scope Submit manuscript

Abstract

We investigate the optimal consumption, portfolio, and life insurance decisions problem of a liquidity constrained household whose preference is given by the CES (constant elasticity of substitution) utility function. By applying the martingale and duality method, we obtain the closed-form solution for the household’s value function and optimal strategies. We provide a rigorous proof for the optimality of the strategies. We exhibit comparative static results of the optimal decisions with respect to the elasticity of substitution between consumption and leisure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Ahn, S., Choi, K.J., Lim, B.H.: Optimal consumption and investment under time-varying liquidity constraints. J. Financ. Quant. Anal. 54, 1643–1681 (2019)

    Article  Google Scholar 

  2. Bensoussan, A., Jang, B.-G., Park, S.: Unemployment risks and optimal retirement in an incomplete market. Oper. Res. 64, 1015–1032 (2016)

    Article  MathSciNet  Google Scholar 

  3. Choi, K.J., Shim, G., Shin, Y.H.: Optimal portfolio, consumption-leisure and retirement choice problem with CES utility. Math. Financ. 18, 445–472 (2008)

    Article  MathSciNet  Google Scholar 

  4. Dybvig, P.H., Liu, H.: Lifetime consumption and investment: retirement and constrained borrowing. J. Econ. Theory 145, 885–907 (2010)

    Article  MathSciNet  Google Scholar 

  5. Dybvig, P.H., Liu, H.: Verification theorems for models of optimal consumption and investment with retirement and constrained borrowing. Math. Oper. Res. 36, 620–635 (2010)

    Article  MathSciNet  Google Scholar 

  6. El Karoui, N., Jeanblanc-Picqué, M.: Optimization of consumption with labor income. Financ. Stoch. 2, 409–440 (1998)

    Article  Google Scholar 

  7. Farhi, E., Panageas, S.: Saving and investing for early retirement: a theoretical analysis. J. Financ. Econ. 83, 87–121 (2007)

    Article  Google Scholar 

  8. He, H., Pagès, H.F.: Labor income, borrowing constraints, and equilibrium asset prices. Econ. Theory 3, 663–696 (1993)

    Article  MathSciNet  Google Scholar 

  9. Jang, B.-G., Koo, H.K., Park, S.: Optimal consumption and investment with insurer default risk. Insur. Math. Econ. 88, 44–56 (2019)

    Article  MathSciNet  Google Scholar 

  10. Koo, H.K.: Consumption and portfolio selection with labor income: a continuous time approach. Math. Financ. 8, 49–65 (1998)

    Article  Google Scholar 

  11. Karatzas, I., Shreve, S.E.: Methods of Mathematical Finance. Springer, New York (1998)

    Book  Google Scholar 

  12. Lee, H.S., Shin, Y.H.: An optimal portfolio, consumption-leisure and retirement choice problem with CES utility: a dynamic programming approach. J. Inequal. Appl. 2015, 319 (2015)

    Article  MathSciNet  Google Scholar 

  13. Lee, H.S., Shim, G., Shin, Y.H.: Borrowing constraints, effective flexibility in labor supply, and portfolio selection. Math. Financ. Econ. 13, 173–208 (2019)

    Article  MathSciNet  Google Scholar 

  14. Lim, B.H., Kwak, M.: The impact of a partial borrowing limit on financial decisions. Quant. Financ. 19, 859–883 (2019)

    Article  MathSciNet  Google Scholar 

  15. Lim, B.H., Shin, Y.H.: Optimal investment, consumption and retirement decision with disutility and borrowing constraints. Quant. Financ. 11, 1581–1592 (2011)

    Article  MathSciNet  Google Scholar 

  16. Merton, R.C.: Lifetime portfolio selection under uncertainty: the continuous-time case. Rev. Econ. Stat. 51, 247–257 (1969)

    Article  Google Scholar 

  17. Merton, R.C.: Optimum consumption and portfolio rules in a continuous-time model. J. Econ. Theory 3, 373–413 (1971)

    Article  MathSciNet  Google Scholar 

  18. Merton, R.C.: An intertemporal capital asset pricing model. Econometrica 41, 867–887 (1973)

    Article  MathSciNet  Google Scholar 

  19. Park, S., Jang, B.: Optimal retirement strategy with a negative wealth constraint. Oper. Res. Lett. 42, 208–212 (2014)

    Article  MathSciNet  Google Scholar 

  20. Vila, J.-L., Zariphopoulou, T.: Optimal consumption and portfolio choice with borrowing constraints. J. Econ. Theory 77, 402–431 (1997)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics and Finance, The University of Suwon, Hwaseong, Republic of Korea

    Byung Hwa Lim

  2. Department of Mathematics, Kwangwoon University, Seoul, Republic of Korea

    Ho-Seok Lee

Authors
  1. Byung Hwa Lim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ho-Seok Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ho-Seok Lee.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Lim was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2017R1E1A1A03071107). The work of Ho-Seok Lee was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2019R1F1A1060853) and by the Research Grant of Kwangwoon University in 2020.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lim, B.H., Lee, HS. Household utility maximization with life insurance: a CES utility case. Japan J. Indust. Appl. Math. 38, 271–295 (2021). https://doi.org/10.1007/s13160-020-00437-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13160-020-00437-9

Keywords

Mathematics Subject Classification

Search

Navigation