Convergence of the Embedded Mean-Variance Optimal Points with Discrete Sampling

28 Pages Posted: 31 Oct 2013 Last revised: 6 Sep 2017

See all articles by Duy-Minh Dang

Duy-Minh Dang

University of Queensland - School of Mathematics and Physics

Peter Forsyth

University of Waterloo - Cheriton School of Computer Science

Yuying Li

University of Waterloo

Date Written: March 18, 2015

Abstract

A numerical technique based on the embedding technique proposed in [21, 33] for dynamic mean-variance (MV) optimization problems may yield spurious points, i.e. points which are not on the efficient frontier. In [27], it is shown that spurious points can be eliminated by examining the left upper convex hull of the solution of the embedded problem. However, any numerical algorithm will generate only a discrete sampling of the solution set of the embedded problem. In this paper, we formally establish that, under mild assumptions, every limit point of a suitably defined sequence of upper convex hulls of the sampled solution of the embedded problem is on the original MV efficient frontier. For illustration, we discuss an MV asset-liability problem under jump diffusions, which is solved using a numerical Hamilton-Jacobi-Bellman partial differential equation approach.

Keywords: mean-variance, scalarization optimization, embedding, Pareto optimal, asset-liability, Hamilton-Jacobi-Bellman (HJB) equation, jump diffusion

JEL Classification: E40, E43, G12, G13, C61, C63

Suggested Citation

Dang, Duy-Minh and Forsyth, Peter and Li, Yuying, Convergence of the Embedded Mean-Variance Optimal Points with Discrete Sampling (March 18, 2015). Available at SSRN: https://ssrn.com/abstract=2346912 or http://dx.doi.org/10.2139/ssrn.2346912

Duy-Minh Dang (Contact Author)

University of Queensland - School of Mathematics and Physics ( email )

Priestly Building
St Lucia
Brisbane, Queesland 4067
Australia

HOME PAGE: http://people.smp.uq.edu.au/Duy-MinhDang/

Peter Forsyth

University of Waterloo - Cheriton School of Computer Science ( email )

Waterloo, Ontario N2L 3G1
Canada

Yuying Li

University of Waterloo ( email )

Waterloo, Ontario N2L 3G1
Canada

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