Predictable Forward Performance Processes: The Binomial Case
23 Pages Posted: 16 Nov 2016 Last revised: 14 Oct 2019
Date Written: January 31, 2019
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: Suggested Citation