Optimal solution of investment problems via linear parabolic equations generated by Kalman filter

TL;DR

This paper develops a method to solve optimal investment problems in markets with unobservable parameters by linking portfolio strategies to solutions of linear parabolic equations derived from Kalman filtering.

Contribution

It introduces a novel approach that expresses optimal strategies through linear parabolic equations with coefficients generated by Kalman filters, for non-observable market parameters.

Findings

Optimal strategies are characterized via solutions to linear parabolic equations.

The approach handles non-linear performance criteria in unobservable market models.

Kalman filter-based coefficients enable practical computation of optimal portfolios.

Abstract

We consider optimal investment problems for a diffusion market model with non-observable random drifts that evolve as an Ito's process. Admissible strategies do not use direct observations of the market parameters, but rather use historical stock prices. For a non-linear problem with a general performance criterion, the optimal portfolio strategy is expressed via the solution of a scalar minimization problem and a linear parabolic equation with coefficients generated by the Kalman filter.