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Unpublished Paper
Portfolio Optimization under Convex Incentive Schemes
Mathematical Sciences Faculty Publications (2013)
  • Stephan Sturm, Worcester Polytechnic Institute
  • Maxim Bichuch
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 o 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,
  • fund manager’s problem,
  • incentive scheme,
  • convex duality,
  • delegated portfolio management portfolio optimization,
  • fund manager’s problem,
  • incentive scheme,
  • convex duality,
  • delegated portfolio management
Publication Date
January 1, 2013
Citation Information
Stephan Sturm and Maxim Bichuch. "Portfolio Optimization under Convex Incentive Schemes" Mathematical Sciences Faculty Publications (2013)
Available at: http://works.bepress.com/stephan_sturm/2/