Author(s)

JingShu Liu

Affiliation(s)

Questrom School of Business, Boston University, Boston 02215, MA, US.

Corresponding Author

JingShu Liu

ABSTRACT

This paper solves the optimal dynamic portfolio choice problem for an ambiguity-averse investor. It introduces a new preference that allows for the separation of risk aversion and ambiguity aversion. The novel representation is based on generalized divergence measures that capture richer forms of model uncertainty than traditional the relative entropy measure. The novel preferences are shown to have a homothetic stochastic differential utility representation. Based on this representation, optimal portfolio policies are derived using numerical algorithms with forward-backward stochastic differential equations. The optimal portfolio policy is shown to contain new hedging motives induced by the investor’s attitude toward model uncertainty. Ambiguity concerns introduce additional horizon effects, increase effective risk aversion, and overall reduce optimal investment in risky assets. These findings have important implications for the design of optimal portfolios in the presence of model uncertainty.

KEYWORDS

Portfolio optimization; Ambiguity aversion; Robust-optimal control; Knightian uncertainty

CITE THIS PAPER

JingShu Liu. Dynamic optimal portfolio choices for robust preferences. World Journal of Economics and Business Research. 2024, 2(1): 47-64. DOI: https://doi.org/10.61784/wjebr3012.

REFERENCES

[1] M Schroder, C. Skiadas. Optimal consumption and portfolio selection with stochastic differential utility. Journal of Economic Theory, 1999, 89(1): 68-126.

[2] DL Ocone, I Karatzas. A generalized Clark representation formula, with application to optimal portfolios. Stochastics and Stochastic Reports, 1991, 34(3-4): 187-220. 

[3] J Detemple, R Garcia, M Rindisbacher. A Monte Carlo method for optimal portfolios. Journal of Finance, 2003, 58(1): 401-446.

[4] E Gobet, J Lemor, X Warin. A regression-based Monte Carlo method to solve backward stochastic differential equations. Annals of Applied Probability, 2005, 15(3): 2172-2202.

[5] H Markowitz. Portfolio selection. Journal of Finance, 1952, 7(1): 77-91.

[6] PA Samuelson. Lifetime portfolio selection by dynamic stochastic programming. Review of Economics and Statistics, 1969, 51(3):239-246.

[7] RC Merton. Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 1971, 3(4): 373-413.

[8] SR Pliska. A stochastic calculus model of continuous trading: Optimal portfolios. Mathematics of Operations Research, 1986, 11(2): 371-383.

[9] I Karatzas, JP Lehoczky, SE Shreve. Optimal portfolio and consumption decisions for a “small investor” on a finite horizon. SIAM Journal on Control and Optimization, 1987, 25(6): 1557-1586.

[10] JC Cox, C Huang. Optimal consumption and portfolio policies when asset prices follow a diffusion process. Journal of Economic Theory, 1989, 49(1):33-83.

[11] L Hansen, T. Sargent. Robust control and model uncertainty. American Eco- nomic Review, 2001, 91(2): 60-66.

[12] RC Merton. On estimating the expected return on the market: An exploratory investigation. Journal of Financial Economics, 1980, 8(4): 323-361.

[13] I Gilboa, D Schmeidler. Max-min expected utility with non-unique priors. Journal of Mathematical Economics, 1989, 18(2): 141-153.

[14] L Epstein, T Wang. Intertemporal asset pricing under Knightian uncertainty. Econometrica, 1994, 62(2): 283-322.

[15] L Epstein, M. Schneider. Recursive multiple priors. Journal of Economic Theory, 2003, 113: 1-31.

[16] L Epstein, M Schneider. Learning under ambiguity. Review of Economic Study, 2007, 74(4)1275-1303.

[17] L Epstein, M Schneider. Ambiguity, information quality and asset pricing. Journal of Finance, 2008, 63(1): 197-228.

[18] P Klibanoff, M Marinacci, S Mukerji. A smooth model of decision making under ambiguity. Econometrica, 2005, 73(6): 1849-1892.

[19] H Chen, N Ju, J Miao. Dynamic asset allocation with ambiguous return predictability. AFA 2010 Atlanta Meeting Paper, 2011.

[20] N Ju, J Miao. Ambiguity, learning, and asset returns. Econometrica, 2012, 80(2): 559-591.

[21] EW Anderson, LP Hansen, TJ Sargent. A quartet of semigroups for model specification, robustness, prices of risk, and model detection. Journal of the Euro- pean Economic Association, 2003, 1(1): 68-123.

[22] C Skiadas. Smooth ambiguity aversion toward small risks and continuous-time recursive utility. Journal of Political Economy, 2013, 121(4): 775-792.

[23] P Maenhout. Robust portfolio rules and asset pricing. Review of Financial Studies, 2004, 17(4): 951-983.

[24] C Skiadas. Robust control and recursive utility. Finance and Stochastics, 2003, 7(4): 475-489.

[25] DJ Meyer, J Meyer. Measuring Risk Aversion. Foundations and trends in microeconomics. Now Publishers, 2006.

[26] JY Campbell, YL Chan, LM Viceira. A multivariate model of strategic asset allocation. Journal of Financial Economics, 2003, 67(1): 41-80.

[27] F Maccheroni, M Marinacci, A Rustichini. Ambiguity aversion, malevolent nature, and the variational representation of preferences. Econometrica, 2006, 74(6): 1447-1498.

[28] J Miao, T Hayashi. Intertemporal substitution and recursive smooth ambiguity preferences. Economics, 2011, 6(3): 423-472.

[29] P Maenhout. Robust portfolio rules and detection-error probabilities for a mean- reverting risk premium. Journal of Economic Theory, 2006, 128(1): 136-163.

[30] J Berger. Statistical Decision Theory and Bayesian Analysis. Springer, 2nd edition, 1985.

[31] D Nualart. The Malliavin Calculus and Related Topics. Springer Verlag, 1995.

[32] NE Karoui, S Peng, MC Quenez. Backward stochastic differential equations in finance. Mathematical Finance, 1997, 7(1): 1-71.

[33] LP Hansen. Large sample properties of generalized method of moments estimators. Econometrica, 1982, 50(4): 1029-1054.

[34] LP Hansen, TJ Sargent. Robustness. Princeton University Press, 2008.

[35] AR Pedersen. A new approach to maximum likelihood estimation for stochastic differential equations based on discrete observations. Scandinavian Journal of Statistics, 1995, 22(1): 55-71.

[36] C Skiadas. Recursive utility and preferences for information. Economic Theory, 1998, 12: 293-312.