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Stochastic Portfolio Optimization With Log Utility

Author

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  • TAO PANG

    (Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA)

Abstract

A portfolio optimization problem on an infinite time horizon is considered. Risky asset price obeys a logarithmic Brownian motion, and the interest rate varies according to an ergodic Markov diffusion process. Moreover, the interest rate fluctuation is correlated with the risky asset price fluctuation. The goal is to choose optimal investment and consumption policies to maximize the infinite horizon expected discounted log utility of consumption. A dynamic programming principle is used to derive the dynamic programming equation (DPE). The explicit solutions for optimal consumption and investment control policies are obtained. In addition, for a special case, an explicit formula for the value function is given.

Suggested Citation

  • Tao Pang, 2006. "Stochastic Portfolio Optimization With Log Utility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(06), pages 869-887.
    • Handle: RePEc:wsi:ijtafx:v:09:y:2006:i:06:n:s0219024906003858
    DOI: 10.1142/S0219024906003858
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    Citations

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    Cited by:

    1. Rohini Kumar & Hussein Nasralah, 2016. "Asymptotic approximation of optimal portfolio for small time horizons," Papers 1611.09300, arXiv.org, revised Feb 2018.
    2. Sheng Delei, 2016. "The Optimal Strategy of Reinsurance-Investment Problem for an Insurer with Dynamic Income Under Stochastic Interest Rate," Journal of Systems Science and Information, De Gruyter, vol. 4(3), pages 244-257, June.
    3. Dai, Darong, 2011. "Wealth Martingale and Neighborhood Turnpike Property in Dynamically Complete Market with Heterogeneous Investors," MPRA Paper 46416, University Library of Munich, Germany.
    4. Lijun Bo & Xindan Li & Yongjin Wang & Xuewei Yang, 2013. "Optimal Investment and Consumption with Default Risk: HARA Utility," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 20(3), pages 261-281, September.
    5. Weiwei Shen & Juliang Yin, 2022. "Optimal Investment and Risk Control Strategies for an Insurer Subject to a Stochastic Economic Factor in a Lévy Market," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2913-2931, December.
    6. Shen, Yang & Siu, Tak Kuen, 2012. "Asset allocation under stochastic interest rate with regime switching," Economic Modelling, Elsevier, vol. 29(4), pages 1126-1136.
    7. Minglian Lin & Indranil SenGupta, 2021. "Analysis of optimal portfolio on finite and small time horizons for a stochastic volatility market model," Papers 2104.06293, arXiv.org.
    8. Mou-Hsiung Chang & Tao Pang & Yipeng Yang, 2011. "A Stochastic Portfolio Optimization Model with Bounded Memory," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 604-619, November.
    9. Zhuo Jin, 2015. "Optimal Debt Ratio and Consumption Strategies in Financial Crisis," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 1029-1050, September.
    10. Jin, Zhuo & Yang, Hailiang & Yin, G., 2015. "Optimal debt ratio and dividend payment strategies with reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 351-363.
    11. Tao Pang & Katherine Varga, 2019. "Portfolio Optimization for Assets with Stochastic Yields and Stochastic Volatility," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 691-729, August.
    12. Darong Dai, 2013. "Wealth Martingale and Neighborhood Turnpike Property In Dynamically Complete Market With Heterogeneous Investors," Economic Research Guardian, Weissberg Publishing, vol. 3(2), pages 86-110, December.

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