ANNUNCIO DI SEMINARIO
Il Prof. Eckhard Platen, professore alla University of Technology di Sydney ed
attuale Presidente della Bachelier Finance Society, terra' il seguente
seminario dalle 14.30 alle 15.30 del martedi' 5 maggio in aula 2BC60 del
Dipartimento di Matematica, via Trieste 63, Padova.
(Si noti lo spostamento dalla originale aula 2AB40 alla 2BC60)
Referente: W. Runggaldier
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TITLE: BENCHMARKED RISK MINIMIZATION
ABSTRACT: 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.)
