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Contemporary Quantitative Finance pp 195–216Cite as

Stochastic Partial Differential Equations and Portfolio Choice

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Abstract

We introduce a stochastic partial differential equation which describes the evolution of the investment performance process in portfolio choice models. The equation is derived for two formulations of the investment problem, namely, the traditional one (based on maximal expected utility of terminal wealth) and the recently developed forward formulation. The novel element in the forward case is the volatility process which is up to the investor to choose. We provide various examples for both cases and discuss the differences and similarities between the different forms of the equation as well as the associated solutions and optimal processes.

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Author information

Authors and Affiliations

  1. BNP Paribas, 10 Harewood Avenue, London, NW1 6AA, UK

    Marek Musiela

  2. Oxford-Man Institute and Mathematical Institute, University of Oxford, 2 Walton Well Road, Oxford, OX2 6ED, UK

    Thaleia Zariphopoulou

  3. Departments of Mathematics and IROM, McCombs School of Business, The University of Texas at Austin, 1 University Station, C1200, Austin, TX, 78712, USA

    Thaleia Zariphopoulou

Authors
  1. Marek Musiela
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  2. Thaleia Zariphopoulou
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Correspondence to Thaleia Zariphopoulou .

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Editors and Affiliations

  1. School of Finance and Economics Department of Mathematical Sciences, The University of Technology, Sydney, P.O. Box 123, Broadway 2007, NSW, Australia

    Carl Chiarella  & Alexander Novikov  & 

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Musiela, M., Zariphopoulou, T. (2010). Stochastic Partial Differential Equations and Portfolio Choice. In: Chiarella, C., Novikov, A. (eds) Contemporary Quantitative Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03479-4_11

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