On Mean-Variance Analysis

TL;DR

This paper addresses mean-variance portfolio optimization involving primary and derivative securities, using delta-gamma approximation to linearize nonlinearities and reduce the problem to a quadratic program, with applications in pricing and hedging.

Contribution

It introduces a delta-gamma approximation method to handle nonlinearities in mean-variance portfolio management with derivatives, enabling quadratic programming solutions.

Findings

Effective linearization of nonlinear portfolio problems

Quadratic programming approach for optimization

Applicability to pricing and hedging in incomplete markets

Abstract

This paper considers the mean variance portfolio management problem. We examine portfolios which contain both primary and derivative securities. The challenge in this context is due to portfolio's nonlinearities. The delta-gamma approximation is employed to overcome it. Thus, the optimization problem is reduced to a well posed quadratic program. The methodology developed in this paper can be also applied to pricing and hedging in incomplete markets.