\documentclass[11pt]{article} \setlength{\oddsidemargin}{0.0truein} \setlength{\evensidemargin}{0.0truein} \setlength{\textwidth}{6.5truein} \setlength{\topmargin}{0.0truein} \setlength{\textheight}{9.0truein} \setlength{\headsep}{0.0truein} \setlength{\headheight}{0.0truein} \setlength{\topskip}{10.0pt} \setlength{\parskip}{5mm} \usepackage{url} \usepackage{amsmath} \usepackage{amssymb} \pagestyle{empty} \begin{document} \begin{center} \textbf{\Large{\textsc{STANFORD UNIVERSITY}}}\\[5pt] \textbf{\Large{\textsc{DEPARTMENT OF STATISTICS}}}\\[5pt] \Large{\textsc{Statistics and Financial Math Seminar}} \end{center} % In the following statements, replace "Time of talk", % "Weekday", and "Date of talk". An example is provided. % If you are not sure about this, just skip this part. \begin{center} % Time of talk, Weekday, Date of talk\\ 4:15 p.m., Tuesday, July 22, 2007\\ Sequoia Hall Room 200\\ (Cookies at 3:45 in 1st Floor Lounge) \end{center} % In the following statements, replace "Name of the speaker" with your % name, "Department Affiliation" with your department affiliation, and %"University Affiliation" with your university affiliation. \begin{center} \textsl{Haipeng Xing} \\ Department of Applied Maths \& Stat\\ State Univ of New York at Stony Brook \end{center} % In the following statements, replace "Title of the talk" % with your title of the talk. \begin{center} \subsection*{Mean-variance portfolio optimization when means and covariances are unknown} \end{center} \noindent Markowitz's celebrated mean-variance portfolio optimization theory assumes that the means and covariances of the underlying asset returns are known. In practice, they are unknown and have to be estimated from historical data. Plugging them into the efficient frontier that assumes know parameters leads to the so-called "Markowitz enigma", which states that portfolio with the "plug-in" efficient frontier can behave badly and be counter-intuitive. We first review different approaches and explain why they fall short of their goal. We then describe a new approach with ideas from stochastic adaptive control and bootstrap resampling. Applications of the new approach to simulated and real data are also given. \end{document}