Predictable Forward Performance Processes: The Binomial Case

23 Pages Posted: 16 Nov 2016 Last revised: 14 Oct 2019

See all articles by Bahman Angoshtari

Bahman Angoshtari

University of Washington

Thaleia Zariphopoulou

University of Texas at Austin - Red McCombs School of Business

Xun Yu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Date Written: January 31, 2019

Abstract

We introduce a new class of forward performance processes that are endogenous and predictable with regards to an underlying market information set and, furthermore, are updated at discrete times. We analyze in detail a binomial model whose parameters are random and updated dynamically as the market evolves. We show that the key step in the construction of the associated predictable forward performance process is to solve a single-period inverse investment problem, namely, to determine, period-by-period and conditionally on the current market information, the end-time utility function from a given initial-time value function. We reduce this inverse problem to solving a functional equation and establish conditions for the existence and uniqueness of its solutions in the class of inverse marginal functions.

Keywords: Optimal investment, forward performance processes, binomial model, inverse investment problem, iterative functional equation

JEL Classification: C61, G11

Suggested Citation

Angoshtari, Bahman and Zariphopoulou, Thaleia and Zhou, Xunyu, Predictable Forward Performance Processes: The Binomial Case (January 31, 2019). Available at SSRN: https://ssrn.com/abstract=2869277 or http://dx.doi.org/10.2139/ssrn.2869277

Bahman Angoshtari (Contact Author)

University of Washington ( email )

Department of Applied Mathematics
Lewis Hall #202, Box 353925
Seattle, WA WA 98105
United States

Thaleia Zariphopoulou

University of Texas at Austin - Red McCombs School of Business ( email )

Austin, TX 78712
United States

Xunyu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

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