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Portfolio Optimization Models on Infinite-Time Horizon

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  • T. Pang

    (North Carolina State University)

Abstract

A portfolio optimization problem on an infinite-time horizon is considered. Risky asset prices obey a logarithmic Brownian motion and interest rates vary according to an ergodic Markov diffusion process. The goal is to choose optimal investment and consumption policies to maximize the infinite-horizon expected discounted hyperbolic absolute risk aversion (HARA) utility of consumption. The problem is then reduced to a one-dimensional stochastic control problem by virtue of the Girsanov transformation. A dynamic programming principle is used to derive the dynamic programming equation (DPE). The subsolution/supersolution method is used to obtain existence of solutions of the DPE. The solutions are then used to derive the optimal investment and consumption policies. In addition, for a special case, we obtain the results using the viscosity solution method.

Suggested Citation

  • T. Pang, 2004. "Portfolio Optimization Models on Infinite-Time Horizon," Journal of Optimization Theory and Applications, Springer, vol. 122(3), pages 573-597, September.
    • Handle: RePEc:spr:joptap:v:122:y:2004:i:3:d:10.1023_b:jota.0000042596.26927.2d
    DOI: 10.1023/B:JOTA.0000042596.26927.2d
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    References listed on IDEAS

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    1. Thaleia Zariphopoulou, 2001. "A solution approach to valuation with unhedgeable risks," Finance and Stochastics, Springer, vol. 5(1), pages 61-82.
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    Cited by:

    1. Baten Md. Azizul & Khalid Ruzelan, 2020. "A Stochastic Control Model of Investment and Consumption with Applications to Financial Economics," Stochastics and Quality Control, De Gruyter, vol. 35(2), pages 43-55, December.
    2. Najafi, Amir Abbas & Pourahmadi, Zahra, 2016. "An efficient heuristic method for dynamic portfolio selection problem under transaction costs and uncertain conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 154-162.
    3. Dariusz Zawisza, 2016. "Smooth solutions to discounted reward control problems with unbounded discount rate and financial applications," Papers 1602.00899, arXiv.org, revised Feb 2016.
    4. 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.
    5. 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.
    6. Rohini Kumar & Hussein Nasralah, 2016. "Asymptotic approximation of optimal portfolio for small time horizons," Papers 1611.09300, arXiv.org, revised Feb 2018.
    7. Benita, Francisco & Nasini, Stefano & Nessah, Rabia, 2022. "A cooperative bargaining framework for decentralized portfolio optimization," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    8. 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.

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