Representation of homothetic forward performance processes in stochastic factor models via ergodic and infinite horizon BSDE

TL;DR

This paper characterizes homothetic forward performance processes in incomplete markets with stochastic factors using ergodic and infinite horizon BSDEs, linking them to risk-sensitive optimization and classical value functions.

Contribution

It introduces a novel representation of forward performance processes via ergodic BSDEs and connects them to infinite horizon BSDEs and risk-sensitive optimization in stochastic factor models.

Findings

Representation of homothetic forward processes using ergodic BSDEs.

Connection established between forward processes and infinite horizon BSDEs.

Linkage of large horizon behavior with classical homothetic value functions.

Abstract

In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic (power, exponential and logarithmic) forward performance processes in factor-form using ergodic BSDE. We also develop a connection between the forward processes and infinite horizon BSDE, and, moreover, with risk-sensitive optimization. In addition, we develop a connection, for large time horizons, with a family of classical homothetic value function processes with random endowments.