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A Benchmark Approach to Portfolio Optimization under Partial Information

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  • Eckhard Platen
  • Wolfgang Runggaldier

Abstract

This paper proposes a filtering methodology for portfolio optimization when some factors of the underlying model are only partially observed. The level of information is given by the observed quantities that are here supposed to be the primary securities and empirical log-price covariations. For a given level of information we determine the growth optimal portfolio, identify locally optimal portfolios that are located on a corresponding Markowitz efficient frontier and present an approach for expected utility maximization. We also present an expected utility indifference pricing approach under partial information for the pricing of nonreplicable contracts. This results in a real world pricing formula under partial information that turns out to be independent of the subjective utility of the investor and for which an equivalent risk neutral probability measure need not exist.
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  • Eckhard Platen & Wolfgang Runggaldier, 2007. "A Benchmark Approach to Portfolio Optimization under Partial Information," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(1), pages 25-43, March.
    • Handle: RePEc:kap:apfinm:v:14:y:2007:i:1:p:25-43
    DOI: 10.1007/s10690-007-9045-x
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    1. Camilla LandÊn, 2000. "Bond pricing in a hidden Markov model of the short rate," Finance and Stochastics, Springer, vol. 4(4), pages 371-389.
    2. Babbs, Simon H. & Nowman, K. Ben, 1999. "Kalman Filtering of Generalized Vasicek Term Structure Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(1), pages 115-130, March.
    3. Rüdiger Frey & Wolfgang J. Runggaldier, 1999. "Risk-minimizing hedging strategies under restricted information: The case of stochastic volatility models observable only at discrete random times," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(2), pages 339-350, October.
    4. Lakner, Peter, 1995. "Utility maximization with partial information," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 247-273, April.
    5. Platen, Eckhard, 2000. "A minimal financial market model," SFB 373 Discussion Papers 2000,91, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    7. Rüdiger Frey & Wolfgang J. Runggaldier, 2001. "A Nonlinear Filtering Approach To Volatility Estimation With A View Towards High Frequency Data," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 199-210.
    8. Jörn Sass & Ulrich Haussmann, 2004. "Optimizing the terminal wealth under partial information: The drift process as a continuous time Markov chain," Finance and Stochastics, Springer, vol. 8(4), pages 553-577, November.
    9. Bhar Ramaprasad & Chiarella Carl & Runggaldier Wolfgang J., 2004. "Inferring the Forward Looking Equity Risk Premium from Derivative Prices," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(1), pages 1-26, March.
    10. Gombani, Andrea & Jaschke, Stefan R. & Runggaldier, Wolfgang J., 2005. "A filtered no arbitrage model for term structures from noisy data," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 381-400, March.
    11. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    12. Eckhard Platen & Wolfgang Runggaldier, 2004. "A Benchmark Approach to Filtering in Finance," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 79-105, March.
    13. Nicole Bäuerle & Ulrich Rieder, 2007. "Portfolio Optimization With Jumps And Unobservable Intensity Process," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 205-224, April.
    14. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 1-22, March.
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    Citations

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    Cited by:

    1. Meriam El Mansour & Emmanuel Lepinette, 2023. "Robust discrete-time super-hedging strategies under AIP condition and under price uncertainty," Papers 2311.08847, arXiv.org.
    2. Mark H.A. Davis & Sébastien Lleo, 2021. "Risk‐sensitive benchmarked asset management with expert forecasts," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1162-1189, October.
    3. Ke Du & Eckhard Platen, 2011. "Three-Benchmarked Risk Minimization for Jump Diffusion Markets," Research Paper Series 296, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Claudio Fontana & Wolfgang J. Runggaldier, 2012. "Diffusion-based models for financial markets without martingale measures," Papers 1209.4449, arXiv.org, revised Feb 2013.
    5. Kazufumi Fujimoto & Hideo Nagai & Wolfgang Runggaldier, 2014. "Expected Log-Utility Maximization Under Incomplete Information and with Cox-Process Observations," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(1), pages 35-66, March.
    6. S'ebastien Lleo & Wolfgang J. Runggaldier, 2023. "On the Separation of Estimation and Control in Risk-Sensitive Investment Problems under Incomplete Observation," Papers 2304.08910, arXiv.org, revised Nov 2023.
    7. Lleo, Sébastien & Runggaldier, Wolfgang J., 2024. "On the separation of estimation and control in risk-sensitive investment problems under incomplete observation," European Journal of Operational Research, Elsevier, vol. 316(1), pages 200-214.

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    More about this item

    Keywords

    Portfolio optimization; Partial information; Filtering; Growth optimal portfolio; Expected utility maximization; Utility indifference pricing; Real world pricing formula; G10; G13; Primary 90A12; Secondary 60G30; 62P20;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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