Optimal Consumption, Leisure and Job Choice under Inflationary Environment

Expand
  • 1 School of Mathematics, Physics and Finance, Anhui Polytechnic University, Wuhu 241000, Anhui, China;
    2 Business School, University of Shanghai for Science and Technology, Shanghai 200093, China

Received date: 2020-10-23

  Revised date: 2021-09-10

  Online published: 2023-02-28

Supported by

This research was supported by the National Natural Science Foundation of China (No. 71571001) and the Natural Science Foundation of Anhui Province (No. KJ2020A0369).

Abstract

The optimal job choice, consumption and portfolio decision-making of economic agents under inflationary environment for a continuous infinite time are studied. The agent's preference is characterized by the Cobb-Douglas utility function with two variables of consumption and leisure. The economic agent invests in three kinds of assets:risk-free bonds, inflation index bonds and risky assets. The agent has two kinds of working conditions:One is the work with high income and little leisure time, and the other is the work with low income and much leisure time. Firstly, the real wealth process after inflation discount is derived by using Itô formula. Then, based on the expected utility maximization standard under any working state, martingale method is adopted to obtain the closed form solution of optimal job choice, consumption and portfolio decision-making. Finally, the effects of wealth and inflation volatility on the optimal consumption and portfolio strategies are quantitatively analyzed by numerical simulation with given parameters.

Cite this article

Yu-Song Zhang, Chen Fei, Hai-Feng Pan, Jian Huang . Optimal Consumption, Leisure and Job Choice under Inflationary Environment[J]. Journal of the Operations Research Society of China, 2023 , 11(1) : 83 -108 . DOI: 10.1007/s40305-021-00369-2

References

[1] Merton, R.C.:Lifetime portfolio selection under uncertainty:the continuous-time case.Rev.Econ.Stat.51(3), 247-257(1969)
[2] Karatzas, I., Lehoczky, J.P., Sethi, S.P., Shreve, S.E.:Explicit solution of a general consumption portfolio problem.Math.Oper.Res.11(2), 261-294(1986)
[3] Karatzas, I., Wang, H.:Utility maximization with discretionary stopping.SIAM J.Control Optim.39(1), 306-329(2000)
[4] He, H., Pearson, N.D.:Consumption and portfolio policies with incomplete markets and short-sale constraints:the infinite dimensional case.J.Econ.Theory 54(2), 259-304(1991)
[5] Wachter, J.A.:Portfolio and consumption decisions under mean-reverting returns:an exact solution for complete markets.J.Financial Quantitative Anal.37(1), 63-91(2002)
[6] Li, Z.F., Yuan, Z.J.:A dynamic mean-variance model of portfolio selection under parameter uncertainty.J.Manag.Sci.13(12), 1-9(2010).(in Chinese)
[7] Li,Z.F.,Yao,H.X.:Dynamicportfolioselectionofriskyassetsunderuncertainexittimeandstochastic market environment.Syst.Eng.Theory Pract.34(11), 2737-2747(2014).(in Chinese)
[8] Liang, X., Guo, J.:Optimal investment, consumption, and life insurance in an incomplete market.Commun.Stat.Theory Methods 45(13), 3884-3903(2016)
[9] Fei, C., Fei, W.Y., Rui, Y.Y., Yan, L.T.:International investment with exchange rate risk.Asia-Pacific J.Account.Econ.(2019).https://doi.org/10.1080/16081625.2019.1569539
[10] Fei, C.:Optimal stochastic control and optimal consumption-portfolio with G-Brownian motion.Acta Mathematicae Applicatae Sinica 44(3) (2021).(in Chinese)
[11] Choi, K.J., Shim, G.:Disutility, optimal retirement, and portfolio selection.Math.Finance 16(2), 443-467(2006)
[12] Choi, K.J., Shim, G., Shin, Y.H.:Optimal portfolio, consumption-leisure and retirement choice problem with CES utility.Math.Finance 18(3), 445-472(2008)
[13] Fei, W.Y.:Optimal consumption-leisure, portfolio and retirement selection based on α-maxmin expected CES utility with ambiguity.Appl.Math.J.Chin.Univ.27(4), 435-454(2012)
[14] Farhi, E., Panageas, S.:Saving and investing for early retirement:a theoretical analysis.J.Financial Econ.83(1), 87-121(2007)
[15] Dybvig, P.H., Liu, H.:Lifetime consumption and investment:retirement and constrained borrowing.J.Econ.Theory 145(3), 885-907(2010)
[16] Lim, B.H., Shin, Y.H.:Optimal investment, consumption and retirement decision with disutility and borrowing constraints.Quantitative Finance 11(10), 1581-1592(2011)
[17] Liu, H.J., Fei, W.Y., Zhu, Y.W., Zhen, A.M.:Optimal consumption-investment and bequest with insurance and retirement under Knightian uncertainty.Oper.Res.Transactions 18(3), 88-98(2014).(in Chinese)
[18] Lee, H.S., Shin, Y.H.:An optimal consumption, investment and voluntary retirement choice problem with disutility and subsistence consumption constraints:a dynamic programming approach.J.Math.Anal.Appl.428(2), 762-771(2015)
[19] Brennan, M.J., Xia, Y.H.:Dynamic asset allocation under inflation.J.Finance 57(3), 1201-1238(2002)
[20] Kothari, S.P., Shanken, J.:Asset allocation with inflation-protected bonds.Financial Anal.J.60(1), 54-70(2004)
[21] Bensoussan, A., Keppo, J., Sethi, S.P.:Optimal consumption and portfolio decisions with partially observed real prices.Math.Finance 19(2), 215-236(2009)
[22] Fei, W.Y., Li, S.J.:On study of optimal consumption and portfolio with inflation under Knightian uncertainty.Chin.J.Eng.Math.29(6), 799-806(2012).(in Chinese)
[23] Yao, H.X., Wu, H.L., Zeng, Y.:Optimal investment strategy for risky assets under unncertain timehorizon and inflation.Syst.Eng.Theory Pract.34(5), 1089-1099(2014).(in Chinese)
[24] Fei, W.Y., Lv, H.Y., Yu, M.X.:Decision making for optimal consumption and portfolio under inflation with mean-reverting process.J.Syst.Eng.29(6), 791-798(2014).(in Chinese)
[25] Fei, W.Y., Cai, Z.Q., Xia, D.F.:Dynamic asset allocation with inflation under jump-diffusion environment.J.Manag.Sci.China 18(8), 83-94(2015).(in Chinese)
[26] Fei, W.Y., Li, Y.H., Xia, D.F.:Optimal investment strategies of hedge funds with incentive fees under inflationary environment.Syst.Eng.Theory Pract.35(11), 2740-2748(2015)
[27] Fei, W.Y.:Optimal consumption and portfolio under inflation and Markovian switching.Stochastics 85(2), 272-285(2013)
[28] Fei, C., Du, H.J., Fei, W.Y., Yan, L.T.:Entrepreneur's investment-consumption and hedging under inflation risk.J.Syst.Eng.34(3), 383-394(2019).(in Chinese)
[29] Fei, C., Fei, W.Y.:Optimal control of Markovian switching systems with applications to portfolio decisions under inflation.Acta Mathematica Scientia 35B(2), 439-458(2015)
[30] Siu, T.K.:Long-term strategic asset allocation with inflation risk and regime switching.Quantitative Finance 11(10), 1565-1580(2011)
[31] Lim, B.H.:The effect of inflation risk and subsistence constraints on portfolio choice.J.Korea Soc.Ind.Appl.Math.17(2), 115-128(2013)
[32] Kwak, M., Lim, B.H.:Optimal portfolio selection with life insurance under inflation risk.J.Bank.Finance 46, 59-71(2014)
[33] Fei, W.Y., Chen, Y.H., Fei, C.:An optimal investment and voluntary retirement choice problem with subsistence consumption constraints under inflations.J.Syst.Eng.35(1), 60-72(2020).(in Chinese)
[34] Fei, W.Y., Zhang, F.H., Yang, X.G.:The impact of inflation on executive's equity incentive and work effort.Chin.J.Manag.Sci.28(11), 1-11(2020).(in Chinese)
[35] Mkaouar, F., Prigent, J.L., Abid, I.:A diffusion model for long-term optimization in the presence of stochastic interest and inflation rates.Comput.Econ.54(1), 367-417(2019)
[36] Wang, P., Li, Z.F., Sun, J.Y.:Robust portfolio choice for a DC pension plan with inflation risk and mean-reverting risk premium under ambiguity.Optimization 70(1), 191-224(2021)
[37] Shim, G., Shin, Y.H.:An optimal job, consumption/leisure, and investment policy.Oper.Res.Lett.42(2), 145-149(2014)
[38] Karatzas, I., Shreve, S.E.:Methods of Mathematical Finance.Springer, New York (1998)
Options
Outlines

/