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Long Time Asymptotics for Optimal Investment

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Book cover Large Deviations and Asymptotic Methods in Finance

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 110))

Abstract

This survey reviews portfolio selection problem for long-term horizon. We consider two objectives: (i) maximize the probability for outperforming a target growth rate of wealth process (ii) minimize the probability of falling below a target growth rate. We study the asymptotic behavior of these criteria formulated as large deviations control problems, that we solve by duality method leading to ergodic risk-sensitive portfolio optimization problems. Special emphasis is placed on linear factor models where explicit solutions are obtained.

Contribution to Springer Proceedings in Asymptotic Methods in Finance (Editors Friz-Gatheral-Gulisashvili-Jacquier-Teichmann), in memory of Peter Laurence.

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Author information

Authors and Affiliations

  1. Laboratoire de Probabilités et Modèles Aléatoires CNRS, UMR 7599, Université Paris Diderot, Paris, France

    Huyên Pham

  2. CREST-ENSAE, Malakoff, France

    Huyên Pham

Authors
  1. Huyên Pham
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Corresponding author

Correspondence to Huyên Pham .

Editor information

Editors and Affiliations

  1. Technische Universität Berlin, Institut für Mathematik, Weierstraß- Institut für Angewandte Analysis und Stochastik, Berlin, Germany

    Peter K. Friz

  2. Department of Mathematics, City University of New York Baruch College, New York, New York, USA

    Jim Gatheral

  3. Department of Mathematics, Ohio University, Athens, Ohio, USA

    Archil Gulisashvili

  4. Department of Mathematics, Imperial College London, London, United Kingdom

    Antoine Jacquier

  5. Department of Mathematics, ETH Zürich, Zürich, Switzerland

    Josef Teichmann

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Pham, H. (2015). Long Time Asymptotics for Optimal Investment. In: Friz, P., Gatheral, J., Gulisashvili, A., Jacquier, A., Teichmann, J. (eds) Large Deviations and Asymptotic Methods in Finance. Springer Proceedings in Mathematics & Statistics, vol 110. Springer, Cham. https://doi.org/10.1007/978-3-319-11605-1_18

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