A Unified Approach to Dynamic Mean-Variance Analysis in Discrete and Continuous Time

Abstract

Motivated by yield curve modeling, we solve dynamic mean-variance efficiency problems in both discrete and continuous time. Our solution applies to both complete and incomplete markets and we do not require the existence of a riskless asset, which is relevant for yield curve modeling. Stochastic market parameters are incorporated using a vector of state variables. In particular for markets with deterministic parameters, we provide explicit solutions. In such markets, where no riskless asset need be present, we describe term-independent uniformly mean-variance efficient investment strategies. For constant parameters we show the existence of a unique, symmetrically distributed, trend stationary, uniformly MV efficient strategy.