Utility Maximization Under Bounded Expected Loss

Abstract

We consider optimal selection of portfolios for utility maximizing investors under joint budget and shortfall risk constraints. The shortfall risk is measured in terms of the expected loss. Depending on the parameters of the risk constraint, we show the existence of an optimal solution and uniqueness of the corresponding Lagrange multipliers. Using Malliavin calculus we also provide the optimal trading strategy.

Keywords:

• Expected shortfall
• Malliavin calculus
• Portfolio optimization
• Risk constraint
• Utility maximization

Mathematics Subject Classification:

• Primary 91B28
• Secondary 60G44

ACKNOWLEDGMENTS

This work was partly supported by the Austrian Science Fund FWF, project P17947-N12. The second author acknowledges support by the Heisenberg Programme of the German Research Foundation DFG. We thank three anonymous referees for their comments which led to a considerable improvement of the article.