Optimal consumption and investment with bounded downside risk measures for logarithmic utility functions

Claudia Kluppelberg (1) , Serguei Pergamenchtchikov (2)

1 Centre Mathématique
2 LMRS - Laboratoire de Mathématiques Raphaël Salem

We investigate optimal consumption problems for a Black-Scholes market under uniform restrictions on Value-at-Risk and Expected Shortfall for logarithmic utility functions. We find the solutions in terms of a dynamic strategy in explicit form, which can be compared and interpreted. This paper continues our previous work, where we solved similar problems for power utility functions.

Mots clés: Black-Scholes model; Capital-at-Risk; Expected Shortfall; logarithmic utility; optimal consumption; portfolio optimization; utility maximization; Value-at-Risk

Domaines: Probabilités [math.PR]

Claudia Kluppelberg, Serguei Pergamenchtchikov. Optimal consumption and investment with bounded downside risk measures for logarithmic utility functions. Walter de Gruyter, pp.428, 2009, Advanced Financial Modelling, H. Albrecher, W. Rungalder and W. Schachermayer. ⟨hal-00454078⟩