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

Sergey Nadtochiy () and Thaleia Zariphopoulou ()
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Sergey Nadtochiy: University of Michigan, Department of Mathematics
Thaleia Zariphopoulou: University of Oxford, Oxford-Man Institute

A chapter in Inspired by Finance, 2014, pp 475-504 from Springer

Abstract: 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.

Keywords: Forward investment performance; Hamilton–Jacobi–Bellman equation; Distortion transformation; Widder theorem; Heston model; 91G20 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-02069-3_22

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DOI: 10.1007/978-3-319-02069-3_22

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