Portfolio Optimization Under Convex Incentive Schemes
39 Pages Posted: 15 Sep 2011 Last revised: 21 Feb 2015
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: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
By Michael J. Brennan and Feifei Li
-
Equilibrium Prices in the Presence of Delegated Portfolio Management
By Domenico Cuoco and Ron Kaniel
-
Portfolio Performance and Agency
By Philip H. Dybvig, Heber Farnsworth, ...
-
Portfolio Performance and Agency
By Philip H. Dybvig, Heber Farnsworth, ...
-
Portfolio Performance and Agency
By Heber Farnsworth, Philip H. Dybvig, ...
-
Portfolio Performance and Agency
By Philip H. Dybvig, Heber Farnsworth, ...
-
Equilibrium Prices in the Presence of Delegated Portfolio Management
By Domenico Cuoco and Ron Kaniel
-
Offsetting the Incentives: Risk Shifting and Benefits of Benchmarking in Money Management
By Suleyman Basak, Anna Pavlova, ...
-
Offsetting the Incentives: Risk Shifting and Benefits of Benchmarking in Money Management
By Suleyman Basak, Anna Pavlova, ...