Optimal consumption and investment with bounded downside risk for power utility functions

Claudia Kluppelberg (1) , Serguei Pergamenchtchikov (2)

1 Centre Mathématique
2 LMRS - Laboratoire de Mathématiques Raphaël Salem

We investigate optimal consumption and investment problems for a Black-Scholes market under uniform restrictions on Value-at-Risk and Expected Shortfall. We formulate various utility maximization problems, which can be solved explicitly. We compare the optimal solutions in form of optimal value, optimal control and optimal wealth to analogous problems under additional uniform risk bounds. Our proofs are partly based on solutions to Hamilton-Jacobi-Bellman equations, and we prove a corresponding verification theorem. \footnotetext{This work was supported by the European Science Foundation through the AMaMeF programme.

Mots clés: Portfolio optimization; Stochastic optimal control; Risk constraints; Value-at-Risk; Expected Shortfall

Domaines: Probabilités [math.PR]

Claudia Kluppelberg, Serguei Pergamenchtchikov. Optimal consumption and investment with bounded downside risk for power utility functions. 2009. ⟨hal-00454072⟩