A numerical approach to solve consumption-portfolio problems with predictability in income, stock prices, and house prices
Tóm tắt
In this paper, I establish a numerical method to solve a generic consumption-portfolio choice problem with predictability in stock prices, house prices, and labor income. I generalize the SAMS method introduced by Bick et al. (Manag Sci 59:485–503, 2013) to state-dependent modifiers. I set up artificial markets to derive closed-form solutions for my life-cycle problem and transform the resulting consumption-portfolio strategies into feasible ones in the true market. To obtain transformed-feasible strategies that are close to the truly, unknown optimal strategies, I introduce state-dependent modifiers. I show that this generalization of the SAMS method reduces the welfare losses from over 10% to less than 2%.
Tài liệu tham khảo
Bick B, Kraft H, Munk C (2013) Solving constrained consumption-investment problems by simulation of artificial market strategies. Manag Sci 59:485–503
Brandt MW, Goyal A, Santa-Clara P, Stroud JR (2005) A simulation approach to dynamic portfolio choice with an application to learning about return predictability. Rev Financ Stud 18:831–873
Campbell JY (2006) Household finance, presidential address to the American Finance Association. J Finance 61:1553–1604
Cochrane JH (2011) Presidential address: discount rates. J Finance 66:1047–1108
Cvitanic J, Karatzas I (1992) Convex duality in constrained portfolio optimization. Ann Appl Probab 2:767–818
Cvitanic J, Goukasian L, Zapatero F (2003) Monte Carlo computation of optimal portfolios in complete markets. J Econ Dyn Control 27:971–986
Detemple JB, Garcia R, Rindisbacher M (2003) A Monte Carlo method for optimal portfolios. J Finance 58:401–446
Fleming W, Soner M (2006) Controlled Markov processes and viscosity solutions, 2nd edn. Springer, Berlin
Heath D, Schweizer M (2000) Martingales versus PDEs in finance: an equivalence result with examples. J Appl Probab 37:947–957
Koijen RSJ, Nijman TE, Werker BJM (2007) Appendix describing the numerical methods used in ”When can life-cycle investors benefit from time-varying bond risk premia?”. Working paper
Koijen RSJ, Nijman TE, Werker BJM (2010) When can life cycle investors benefit from time-varying bond risk premia? Rev Financ Stud 23:741–780
Kraft H, Munk C (2011) Optimal housing, consumption, and investment decisions over the life-cycle. Manag Sci 57:1025–1041
Kraft H, Munk C, Weiss F (2019) Predictors and portfolios over the life cycle. J Bank Finance 100:1–27
Liu J (2007) Portfolio selection in stochastic environments. Rev Financ Stud 20:1–39
Longstaff FA, Schwartz ES (2001) Valuing American options by simulation: a simple least-squares approach. Rev Financ Stud 14:113–147
Merton RC (1969) Lifetime Portfolio selection under uncertainty: the continuous-time case. Rev Econ Stat 51:247–257
Merton RC (1971) Optimum consumption and portfolio rules in a continuous-time model. J Econ Theory 3:373–413
Schroeder P, Schober P, Wittum G (2013) Dimension-wise decompositions and their efficient parallelization. Recent Dev Comput Finance Interdiscip Math Sci 14:445–472
Wachter JA (2002) Portfolio and consumption decisions under mean-reverting returns: an exact solution for complete markets. J Financ Quant Anal 37:63–91