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Optimal Equivalent Probability Measures under Enlarged Filtrations

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  • Markus Hess

    (Université Libre de Bruxelles)

Abstract

In a general jump-diffusion Radon–Nikodym setup with stochastic Girsanov processes, we derive optimal equivalent probability measures. Optimality is measured in terms of minimum relative entropy and also by more general divergence concepts. We further provide an anticipative sufficient stochastic minimum principle and derive optimal equivalent probability measures under various enlarged filtration approaches.

Suggested Citation

  • Markus Hess, 2019. "Optimal Equivalent Probability Measures under Enlarged Filtrations," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 813-839, December.
    • Handle: RePEc:spr:joptap:v:183:y:2019:i:3:d:10.1007_s10957-019-01581-0
    DOI: 10.1007/s10957-019-01581-0
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    References listed on IDEAS

    as
    1. Markus Hess, 2018. "Pricing Temperature Derivatives Under Weather Forecasts," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-34, August.
    2. Freddy Delbaen & Peter Grandits & Thorsten Rheinländer & Dominick Samperi & Martin Schweizer & Christophe Stricker, 2002. "Exponential Hedging and Entropic Penalties," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 99-123, April.
    3. Thorsten Rheinlander & Gallus Steiger, 2006. "The minimal entropy martingale measure for general Barndorff-Nielsen/Shephard models," Papers math/0610219, arXiv.org.
    4. Thomas Goll & Ludger Rüschendorf, 2001. "Minimax and minimal distance martingale measures and their relationship to portfolio optimization," Finance and Stochastics, Springer, vol. 5(4), pages 557-581.
    5. Marco Frittelli, 2000. "The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 39-52, January.
    6. Rheinlander, Thorsten & Steiger, Gallus, 2006. "The minimal entropy martingale measure for general Barndorff-Nielsen/Shephard models," LSE Research Online Documents on Economics 16351, London School of Economics and Political Science, LSE Library.
    7. Giulia Di Nunno & Thilo Meyer-Brandis & Bernt Øksendal & Frank Proske, 2006. "Optimal portfolio for an insider in a market driven by Levy processes," Quantitative Finance, Taylor & Francis Journals, vol. 6(1), pages 83-94.
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    More about this item

    Keywords

    Stochastic optimization problem; Stochastic maximum/minimum principle; Relative entropy; Radon–Nikodym density; Lévy process; Enlarged filtration; Stochastic differential equation;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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