Seminario: Benchmarked risk minimization

Martedì 5 Maggio 2015, ore 14:30 - Aula 2BC60 - Eckhard Platen



Martedì 5 Maggio 2015 alle ore 14:30 in Aula 2BC60 Eckhard Platen (University of Technology, Sydney - Presidente della Bachelier Finance Society), terrà un seminario dal titolo "Benchmarked risk minimization".

The paper discusses the problem of hedging not perfectly replicable contingent claims by using a benchmark, the numeraire portfolio, as reference unit. The proposed concept of benchmarked risk minimization generalizes classical risk minimization, pioneered by Foellmer, Sondermann and Schweizer. The latter relies on a quadratic criterion, requesting the square integrability of contingent claims and the existence of an equivalent risk neutral probability measure. The proposed concept of benchmarked risk minimization avoids these restrictive assumptions. It employs the real world probability measure as pricing measure
and identifies the minimal possible price for the hedgeable part of a contingent claim. Furthermore, the resulting benchmarked profit and loss is only driven by nontraded uncertainty and forms a martingale that starts at zero. Benchmarked profit and losses, when pooled and sufficiently independent, become in total negligible. This property is highly desirable from a risk management point of view. It is making asymptotically benchmarked risk minimization the least expensive method for pricing and hedging of an increasing number of not fully replicable benchmarked contingent claims.
(Joint work with Ke Du.)