Long Term Optimal Investment in Matrix Valued Factor Models

TL;DR

This paper investigates long-term investment strategies within matrix-valued factor models, establishing conditions for convergence of value functions and strategies, and extending affine models to non-affine settings using PDE analysis.

Contribution

It introduces explicit conditions for convergence in matrix-valued factor models and extends affine models to non-affine cases using PDE techniques.

Findings

Convergence of value functions and strategies as horizon approaches infinity.

Extension of affine models to non-affine settings.

Existence of non-exponentially affine value functions in matrix models.

Abstract

Long term optimal investment problems are studied in a factor model with matrix valued state variables. Explicit parameter restrictions are obtained under which, for an isoelastic investor, the finite horizon value function and optimal strategy converge to their long-run counterparts as the investment horizon approaches infinity. This convergence also yields portfolio turnpikes for general utilities. By using results on large time behaviour of semi-linear partial differential equations, our analysis extends affine models, where the Wishart process drives investment opportunities, to a non-affine setting. Furthermore, in the affine setting, an example is constructed where the value function is not exponentially affine, in contrast to models with vector-valued state variables.