Stochastic Partial Differential Equations and Portfolio Choice

  • Marek Musiela
  • Thaleia ZariphopoulouEmail author


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.


Optimal Portfolio Stochastic Volatility Incomplete Market Stochastic Partial Differential Equation Portfolio Choice 
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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.BNP ParibasLondonUK
  2. 2.Oxford-Man Institute and Mathematical InstituteUniversity of OxfordOxfordUK
  3. 3.Departments of Mathematics and IROM, McCombs School of BusinessThe University of Texas at AustinAustinUSA

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