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Portfolio Optimization in Incomplete Markets and Price Constraints Determined by Maximum Entropy in the Mean

Author

Listed:
  • Argimiro Arratia

    (Barcelona Tech (UPC))

  • Henryk Gzyl

    (IESA)

Abstract

A solution to a portfolio optimization problem is always conditioned by constraints on the initial capital and the price of the available market assets. If a risk neutral measure is known, then the price of each asset is the discounted expected value of the asset’s price under this measure. But if the market is incomplete, the risk neutral measure is not unique, and there is a range of possible prices for each asset, which can be identified with bid-ask ranges. We present in this paper an effective method to determine the current prices of a collection of assets in incomplete markets, and such that these prices comply with the cost constraints for a portfolio optimization problem. Our workhorse is the method of maximum entropy in the mean to adjust a distortion function from bid-ask market data. This distortion function plays the role of a risk neutral measure, which is used to price the assets, and the distorted probability that it determines reproduces bid-ask market values. We carry out numerical examples to study the effect on portfolio returns of the computation of prices of the assets conforming the portfolio with the proposed methodology.

Suggested Citation

  • Argimiro Arratia & Henryk Gzyl, 2020. "Portfolio Optimization in Incomplete Markets and Price Constraints Determined by Maximum Entropy in the Mean," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 929-952, December.
    • Handle: RePEc:kap:compec:v:56:y:2020:i:4:d:10.1007_s10614-019-09954-3
    DOI: 10.1007/s10614-019-09954-3
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    References listed on IDEAS

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    1. Wu, Xianyi & Wang, Jinglong, 2003. "On Characterization of Distortion Premium Principle," ASTIN Bulletin, Cambridge University Press, vol. 33(1), pages 1-10, May.
    2. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    3. Dilip B. Madan, 2016. "Conic Portfolio Theory," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-42, May.
    4. Madan,Dilip & Schoutens,Wim, 2016. "Applied Conic Finance," Cambridge Books, Cambridge University Press, number 9781107151697.
    5. Wang, Shaun S. & Young, Virginia R. & Panjer, Harry H., 1997. "Axiomatic characterization of insurance prices," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 173-183, November.
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