Portfolio Optimization Under Convex Incentive Schemes

39 Pages Posted: 15 Sep 2011 Last revised: 21 Feb 2015

See all articles by Maxim Bichuch

Maxim Bichuch

Johns Hopkins University

Stephan Sturm

Worcester Polytechnic Institute (WPI) - Department of Mathematical Sciences

Date Written: October 28, 2013

Abstract

We consider the terminal wealth utility maximization problem from the point of view of a portfolio manager who is paid by an incentive scheme, which is given as a convex function g of the terminal wealth. The manager's own utility function U is assumed to be smooth and strictly concave, however the resulting utility function U \circ g fails to be concave. As a consequence, the problem considered here does not fit into the classical portfolio optimization theory. Using duality theory, we prove wealth-independent existence and uniqueness of the optimal portfolio in general (incomplete) semimartingale markets as long as the unique optimizer of the dual problem has a continuous law. In many cases, this existence and uniqueness result is independent of the incentive scheme and depends only on the structure of the set of equivalent local martingale measures. As examples, we discuss (complete) one-dimensional models as well as (incomplete) lognormal mixture and popular stochastic volatility models. We also provide a detailed analysis of the case where the unique optimizer of the dual problem does not have a continuous law, leading to optimization problems whose solvability by duality methods depends on the initial wealth of the investor.

Keywords: portfolio optimization, hedgefund manager's problem, incentive scheme, convex duality, incomplete market, stochastic volatility model

JEL Classification: G11

Suggested Citation

Bichuch, Maxim and Sturm, Stephan, Portfolio Optimization Under Convex Incentive Schemes (October 28, 2013). Finance Stochastics 18:4, pp. 873-915 (2014), Available at SSRN: https://ssrn.com/abstract=1926976 or http://dx.doi.org/10.2139/ssrn.1926976

Maxim Bichuch

Johns Hopkins University ( email )

Baltimore, MD 20036-1984
United States

Stephan Sturm (Contact Author)

Worcester Polytechnic Institute (WPI) - Department of Mathematical Sciences ( email )

United States
5088315921 (Phone)
5088315824 (Fax)

HOME PAGE: http://users.wpi.edu/~ssturm

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
111
Abstract Views
1,298
rank
303,349
PlumX Metrics