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Stochastic Partial Differential Equations and Portfolio Choice

In: Contemporary Quantitative Finance

Author

Listed:
  • Marek Musiela

    (BNP Paribas)

  • Thaleia Zariphopoulou

    (University of Oxford, Oxford-Man Institute and Mathematical Institute
    The University of Texas at Austin, Departments of Mathematics and IROM, McCombs School of Business)

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.

Suggested Citation

  • Marek Musiela & Thaleia Zariphopoulou, 2010. "Stochastic Partial Differential Equations and Portfolio Choice," Springer Books, in: Carl Chiarella & Alexander Novikov (ed.), Contemporary Quantitative Finance, pages 195-216, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-03479-4_11
    DOI: 10.1007/978-3-642-03479-4_11
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