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Optimal trading strategy for an investor: the case of partial information

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  • Lakner, Peter
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    Abstract

    We shall address here the optimization problem of an investor who wants to maximize the expected utility from terminal wealth. The novelty of this paper is that the drift process and the driving Brownian motion appearing in the stochastic differential equation for the security prices are not assumed to be observable for investors in the market. Investors observe security prices and interest rates only. The drift process will be modelled by a Gaussian process, which in a special case becomes a multi-dimensional mean-reverting Ornstein-Uhlenbeck process. The main result of the paper is an explicit representation for the optimal trading strategy for a wide range of utility functions.

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    File URL: http://www.sciencedirect.com/science/article/B6V1B-3V575RN-R/2/746039797dec129d36a6affb46c1e877
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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 76 (1998)
    Issue (Month): 1 (August)
    Pages: 77-97

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    Handle: RePEc:eee:spapps:v:76:y:1998:i:1:p:77-97

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    Related research

    Keywords: Utility function Security prices and their filtration Trading strategy Optimization Gradient operator Clark's formula;

    References

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    1. Darrell Duffie & William Zame, 1988. "The Consumption-Based Capital Asset Pricing Model," Discussion Papers 88-10, University of Copenhagen. Department of Economics.
    2. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    3. He, Hua & Pearson, Neil D., 1991. "Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case," Journal of Economic Theory, Elsevier, vol. 54(2), pages 259-304, August.
    4. Dothan, Michael U & Feldman, David, 1986. " Equilibrium Interest Rates and Multiperiod Bonds in a Partially Observable Economy," Journal of Finance, American Finance Association, vol. 41(2), pages 369-82, June.
    5. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-84, March.
    6. Lakner, Peter, 1995. "Utility maximization with partial information," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 247-273, April.
    7. Detemple, Jerome B., 1991. "Further results on asset pricing with incomplete information," Journal of Economic Dynamics and Control, Elsevier, vol. 15(3), pages 425-453, July.
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    Citations

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    Cited by:
    1. Albina Danilova & Michael Monoyios & Andrew Ng, 2009. "Optimal investment with inside information and parameter uncertainty," Papers 0911.3117, arXiv.org, revised Feb 2010.
    2. Jianjun Miao, . "Ambiguity, Risk and Portfolio Choice under Incomplete Information," Boston University - Department of Economics - Working Papers Series wp2009-019, Boston University - Department of Economics.
    3. Huang, Jianhui & Wang, Guangchen & Wu, Zhen, 2010. "Optimal premium policy of an insurance firm: Full and partial information," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 208-215, October.
    4. Liu, Hening, 2011. "Dynamic portfolio choice under ambiguity and regime switching mean returns," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 623-640, April.
    5. Michael Mania & Marina Santacroce, 2010. "Exponential utility maximization under partial information," Finance and Stochastics, Springer, vol. 14(3), pages 419-448, September.
    6. Yao, Jing & Li, Duan, 2013. "Bounded rationality as a source of loss aversion and optimism: A study of psychological adaptation under incomplete information," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 18-31.
    7. Liang, Zhibin & Bayraktar, Erhan, 2014. "Optimal reinsurance and investment with unobservable claim size and intensity," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 156-166.
    8. Jinqiang Yang & Zhaojun Yang, 2012. "Consumption Utility-Based Pricing and Timing of the Option to Invest with Partial Information," Computational Economics, Society for Computational Economics, vol. 39(2), pages 195-217, February.
    9. Jörn Sass & Ralf Wunderlich, 2010. "Optimal portfolio policies under bounded expected loss and partial information," Computational Statistics, Springer, vol. 72(1), pages 25-61, August.
    10. Becheri, I.G., 2012. "Limiting experiments for panel-data and jump-diffusion models," Open Access publications from Tilburg University urn:nbn:nl:ui:12-5661649, Tilburg University.
    11. Covello, D. & Santacroce, M., 2010. "Power utility maximization under partial information: Some convergence results," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 2016-2036, September.
    12. Xiang Yu, 2011. "An Explicit Example Of Optimal Portfolio-Consumption Choices With Habit Formation And Partial Observations," Papers 1112.2939, arXiv.org, revised Aug 2012.
    13. Tomas Björk & Mark Davis & Camilla Landén, 2010. "Optimal investment under partial information," Computational Statistics, Springer, vol. 71(2), pages 371-399, April.
    14. Wolfgang Putschögl & Jörn Sass, 2008. "Optimal consumption and investment under partial information," Decisions in Economics and Finance, Springer, vol. 31(2), pages 137-170, November.
    15. Michael Boguslavsky & Elena Boguslavskaya, 2003. "Optimal Arbitrage Trading," Finance 0309012, EconWPA.
    16. Liang, Zhibin & Yuen, Kam Chuen & Guo, Junyi, 2011. "Optimal proportional reinsurance and investment in a stock market with Ornstein-Uhlenbeck process," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 207-215, September.
    17. Peng, Xingchun & Hu, Yijun, 2013. "Optimal proportional reinsurance and investment under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 416-428.
    18. R\"udiger Frey & Abdelali Gabih & Ralf Wunderlich, 2013. "Portfolio Optimization under Partial Information with Expert Opinions: a Dynamic Programming Approach," Papers 1303.2513, arXiv.org, revised Feb 2014.
    19. Michael Mania & Marina Santacroce, 2008. "Exponential Utility Maximization under Partial Information," ICER Working Papers - Applied Mathematics Series 24-2008, ICER - International Centre for Economic Research.

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