Equilibrium consumption and portfolio decisions with stochastic discount rate and time-varying utility functions
Tóm tắt
This paper studies a multi-period investment–consumption optimization problem with a stochastic discount rate and a time-varying utility function, which are governed by a Markov-modulated regime switching model. The investment is dynamically reallocated between one risk-free asset and one risky asset. The problem is time inconsistent due to the stochastic discount rate. An analytical equilibrium solution is established by resorting to a game theoretical framework. Numerous sensitivity analyses and numerical examples are provided to demonstrate the effects of the stochastic discount rate and time-varying utility coefficients on the decision-maker’s investment–consumption behavior. Our results show that many properties which are satisfied in the classical models do not hold any more due to either the stochastic discount rate or the time-varying utility function.
Tài liệu tham khảo
Ainslie GW (1992) Picoeconomics. Cambridge University Press, Cambridge
Barro RJ (1999) Ramsey meets Laibson in the neoclasical growth model. Q J Econ 114:1125–1152
Björk T, Murgoci A (2014) A theory of Markovian time-inconsistent stochastic control in discrete time. Finance Stoch 18:545–592
Björk T, Murgoci A, Zhou XY (2014) Mean variance portfolio optimization with state dependent risk aversion. Math Finance 24:1–24
Campbell JY, Viceira LM (2001) Strategic asset allocation: portfolio choice for long-term investors. Oxford University Press, New York
Çanakoğlu E, Özekici S (2009) Portfolio selection in stochastic markets with exponential utility functions. Ann Oper Res 166:281–297
Çanakoğlu E, Özekici S (2010) Portfolio selection with stochastic markets with HARA utility functions. Eur J Oper Res 201:520–536
Çanakoğlu E, Özekici S (2012) HARA frontiers of optimal portfolios in stochastic markets. Eur J Oper Res 221:129–137
Chen ZP (2005) Multiperiod consumption and portfolio decisions under the multivariate GARCH model with transaction costs and CVaR-based risk control. OR Spectr 27:603–632
Cheung KC, Yang HL (2004) Asset allocation with regime-switching: discrete-time case. ASTIN Bull 34:247–257
Cheung KC, Yang HL (2007) Optimal investment–consumption strategy in discrete-time model with regime switching. Discrete Contin Dyn Syst 8:315–332
Cocco JF, Gomes FJ, Maenhout PJ (2005) Consumption and portfolio choice over the life cycle. Rev Financ Stud 18:491–533
Ekeland I, Lazrak A (2006) Being serious about non-commitment: subgame perfect equilibrium in continuous time. Working paper. http://arxiv.org/abs/math/0604264
Ekeland I, Pirvu TA (2008) Investment and consumption without commitment. Math Financ Econ 2:57–86
Ekeland I, Mbodji O, Pirvu TA (2012) Time-consistent portfolio management. SIAM J Financ Math 3:1–32
Frederick S, Loewenstein G, O’Donoghue T (2002) Time discounting and time preference: a critical review. J Econ Lit 40:351–401
Goldman SM (1980) Consistent plans. Rev Econ Stud 47:533–537
Grenadier SR, Wang N (2007) Investment under uncertainty and time-inconsistent preferences. J Financ Econ 84(1):2–39
Hamilton JD (1989) A new approach to the economic analysis of non-stationary time series. Econometrica 57:357–384
Harris C, Laibson D (2013) Instantaneous gratification. Q J Econ 128(1):205–248
Harrison GW, Lau MI, Williams MB (2002) Estimating individual discount rates in Denmark: a field experiment. Am Econ Rev 92:1606–1617
Hsiaw A (2013) Goal-setting and self-control. J Econ Theory 148(2):601–626
Karatzas I, Shreve SE (1998) Methods of mathematical finance. Springer, New York
Kronborg MT, Steffensen M (2015) Inconsistent investment and consumption problems. Appl Math Optim 71:473–515
Kryger EM, Steffensen M (2010) Some solvable portfolio problems with quadratic and collective objectives. Working paper. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1577265
Li ZF, Tan KS, Yang HL (2008) Multiperiod optimal investment–consumption strategies with mortality risk and environment uncertainty. North Am Actuar J 12:47–64
Loewenstein G, Prelec D (1992) Anomalies in intertemporal choice: evidence and an interpretation. Q J Econ 107:573–597
Marín-Solano J, Navas J (2009) Non-constant discounting in finite horizon: the free terminal time case. J Econ Dyn Control 33:666–675
Marín-Solano J, Navas J (2010) Consumption and portfolio rules for time-inconsistent investors. Eur J Oper Res 201:860–872
Merton RC (1969) Lifetime portfolio selection under uncertainty: the continuous-time case. Rev Econ Stat 51:247–257
Merton RC (1971) Optimal consumption and portfolio rules in a continuous-time model. J Econ Theory 3:373–413
Pirvu TA, Zhang HY (2014) Investment–consumption with regime-switching discount rates. Math Soc Sci 71:142–150
Pollak RA (1968) Consistent planning. Rev Econ Stud 35:201–208
Read D, Read NL (2004) Time discounting over the lifespan. Organ Behav Hum Decis Process 94:22–32
Richard S (1975) Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model. J Financ Econ 2:187–203
Samuelson PA (1969) Lifetime portfolio selection by dynamic stochastic programming. Rev Econ Stat 51:239–246
Strotz RH (1956) Myopia and inconsistency in dynamic utility maximization. Rev Econ Stud 23:165–180
Thaler R (1981) Some empirical evidence on dynamic inconsistency. Econ Lett 8:201–207
Wang J, Forsyth PA (2011) Continuous time mean-variance asset allocation: a time-consistent strategy. Eur J Oper Res 209:184–201
Wei J, Wong KC, Yam SCP, Yung SP (2013) Markowitz’s mean-variance asset-liability management with regime switching: a time-consistent approach. Insurance Math Econ 53:281–291
Weng C (2013) Constant proportion portfolio insurance under regime switching exponential Lévy process. Insurance Math Econ 52(3):508–521
Weng C (2014) Discrete-time CPPI under transaction cost and regime switching. Working paper. http://ssrn.com/abstract=2432233
Wu HL, Li ZF (2012) Multi-period mean-variance portfolio selection with regime switching and a stochastic cash flow. Insurance Math Econ 50:371–384
Zeng Y, Li ZF (2011) Optimal time-consistent investment and reinsurance policies for mean-variance insurers. Insurance Math Econ 49:145–154
Zou Z, Chen S, Wedge L (2014) Finite horizon consumption and portfolio decisions with stochastic hyperbolic discounting. J Math Econ 52:70–80