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Dynamic Asset Allocation And Consumption Choice In Incomplete Markets

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  • SASHA F. STOIKOV
  • THALEIA ZARIPHOPOULOU

Abstract

We study the optimal investment and consumption problem of a CRRA investor when the drift and volatility of the stock are driven by a correlated factor. The myopic and non‐myopic components of the optimal portfolio process are characterised in terms of the market price of traded and non‐traded risk of the minimax martingale measure. We find that the optimal policies depend crucially on the nature of the agent, aggressive versus conservative, and the market incompleteness, improving versus deteriorating investment opportunities. Furthermore, we show that the original problem cannot be decomposed into a pure consumption and a pure terminal wealth problem, unless the market is complete.

Suggested Citation

  • Sasha F. Stoikov & Thaleia Zariphopoulou, 2005. "Dynamic Asset Allocation And Consumption Choice In Incomplete Markets," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 414-454, December.
    • Handle: RePEc:bla:ausecp:v:44:y:2005:i:4:p:414-454
    DOI: 10.1111/j.1467-8454.2005.00269.x
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    References listed on IDEAS

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    1. George Chacko & Luis M. Viceira, 2005. "Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets," The Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1369-1402.
    2. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    3. Louis Kaplow, 2005. "The Value of a Statistical Life and the Coefficient of Relative Risk Aversion," Journal of Risk and Uncertainty, Springer, vol. 31(1), pages 23-34, July.
    4. Campbell, John Y. & Chacko, George & Rodriguez, Jorge & Viceira, Luis M., 2004. "Strategic asset allocation in a continuous-time VAR model," Journal of Economic Dynamics and Control, Elsevier, vol. 28(11), pages 2195-2214, October.
    5. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    6. Kris Jacobs, 2002. "The Rate of Risk Aversion May Be Lower Than You Think," CIRANO Working Papers 2002s-08, CIRANO.
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    Cited by:

    1. Marcel Nutz, 2009. "The Opportunity Process for Optimal Consumption and Investment with Power Utility," Papers 0912.1879, arXiv.org, revised Jun 2010.
    2. Ariel Neufeld & Marcel Nutz, 2015. "Robust Utility Maximization with L\'evy Processes," Papers 1502.05920, arXiv.org, revised Mar 2016.
    3. Zongxia Liang & Ming Ma, 2020. "Robust consumption‐investment problem under CRRA and CARA utilities with time‐varying confidence sets," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 1035-1072, July.
    4. Mellios, Constantin & Six, Pierre & Lai, Anh Ngoc, 2016. "Dynamic speculation and hedging in commodity futures markets with a stochastic convenience yield," European Journal of Operational Research, Elsevier, vol. 250(2), pages 493-504.
    5. Irarrazabal, Alfonso A. & Ma, Lin, 2018. "Optimal Asset Allocation for Commodity Sovereign Wealth Funds," Working Paper Series 11-2018, Norwegian University of Life Sciences, School of Economics and Business.
    6. Josa-Fombellida, Ricardo & Navas, Jorge, 2020. "Time consistent pension funding in a defined benefit pension plan with non-constant discounting," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 142-153.
    7. Hans Follmer & Alexander Schied, 2013. "Probabilistic aspects of finance," Papers 1309.7759, arXiv.org.
    8. Andrew Papanicolaou, 2018. "Backward SDEs for Control with Partial Information," Papers 1807.08222, arXiv.org.

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