Mean-Variance Portfolio Choice with Uncertain Variance-Covariance Matrix

Abstract

Expected returns, variances, and co-variances are key inputs of mean-variance portfolio selection problems. In traditional mean-variance portfolio models, the model uncertainty is excluded a priori. But in practice, these parameters are not known a priori and are usually estimated with error. Current researches incorporate the model uncertainty into the mean-variance framework but mainly focus on the uncertain means. The aim of this dissertation is to incorporate uncertain variance-covariance into mean-variance portfolio model via the concept of ambiguity and ambiguity aversion. The approaches developed in this study numerically compare the impact from return ambiguity and variance ambiguity. In particular, re-examine if uncertain variance-covariance can lead to "No-Participation in Stock Market" and/or "Home Bias" via stock indexes data.

Goal Achieving Probabilities of Mean-Variance Strategies in a Market with Regime-Switching Volatility

“…In his seminal paper [1], Nobel prize laureate Markowitz introduced the myopic (single period) mean-variance portfolio management problem where one calibrates the amount of wealth invested in risky assets (stocks) and a riskless asset (bond) in such a way that it minimizes the variance of a terminal wealth while targeting an average end return. Since then, scores of innovative research problems arose related to his original static model as well as dynamic extensions in both discrete and continuous time, as seen for example in the following recent papers: [2] [3] [4].…”