Optimal portfolio series formula under dynamic appreciation rate uncertainty

Srdjan D. Stojanovic

Abstract

ABSTRACT

A closed-form series solution formula for the problem of optimal portfolio diversification under dynamic (possibly, long-term-memory) appreciation rate uncertainty, for an investor with Hara utility, is found. To that end a calculus of variations method, recently introduced by the author, was extended. The usefulness of the obtained result is examined by means of example solutions to a few guiding problems. To that end we also introduce the notion of T-truncated fractional Brownian motion and study its series expansions.