Predictable Forward Performance Processes: Infrequent Evaluation and Applications to Human-Machine Interactions

TL;DR

This paper develops a mathematical framework for predictable forward processes in financial trading, especially when evaluations are infrequent, and explores their applications in human-machine interactions like automated trading and robo-advising.

Contribution

It introduces a new method to construct predictable forward processes with explicit solutions, highlighting their myopic nature and applying them to optimize human-machine interaction schedules.

Findings

Explicit construction of predictable forward processes under certain conditions

Demonstration of the myopic property of these processes

Application to optimize human-agent interaction schedules in trading

Abstract

We study discrete-time predictable forward processes when trading times do not coincide with performance evaluation times in a binomial tree model for the financial market. The key step in the construction of these processes is to solve a linear functional equation of higher order associated with the inverse problem driving the evolution of the predictable forward process. We provide sufficient conditions for the existence and uniqueness and an explicit construction of the predictable forward process under these conditions. Furthermore, we find that these processes are inherently myopic in the sense that optimal strategies do not make use of future model parameters even if these are known. Finally, we argue that predictable forward preferences are a viable framework to model human-machine interactions occuring in automated trading or robo-advising. For both applications, we determine an optimal interaction schedule of a human agent interacting infrequently with a machine that is in charge of trading.