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A Class of Homothetic Forward Investment Performance Processes with Non-zero Volatility

In: Inspired by Finance

Author

Listed:
  • Sergey Nadtochiy

    (University of Michigan, Department of Mathematics)

  • Thaleia Zariphopoulou

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

Abstract

We study forward investment performance processes with non-zero forward volatility. We focus on the class of homothetic preferences in a single stochastic factor model. The forward performance process is represented in a closed-form via a deterministic function of the wealth and the stochastic factor. This function is, in turn, given as a distortion transformation of the solution to a linear ill-posed problem. We analyze the solutions of this problem in detail. We, also, provide two examples for specific dynamics of the stochastic factor, specifically, log-mean reverting and Heston-type dynamics.

Suggested Citation

  • Sergey Nadtochiy & Thaleia Zariphopoulou, 2014. "A Class of Homothetic Forward Investment Performance Processes with Non-zero Volatility," Springer Books, in: Yuri Kabanov & Marek Rutkowski & Thaleia Zariphopoulou (ed.), Inspired by Finance, edition 127, pages 475-504, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-02069-3_22
    DOI: 10.1007/978-3-319-02069-3_22
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