Project E2: "Securitization: assessment of external risk factors"
Project head: Prof. Ulrich Horst and Prof. Peter Imkeller
Research staff: Dr. Anthony Réveillac and Dipl. Math. Jianing Zhang
Former members: Prof. Stefan Ankirchner (Professor at the University of Bonn); Dipl. Math. Gonçalo Dos Reis (PostDoc at Ecole Polytechnique Paris)
Project Aim
The financial and insurance risk in commodities and energy products
generated by natural phenomena such as weather and climate is exogenous
from the perspective of financial markets. Contracts such as
derivatives written on non-tradable risk of this type therefore can be
seen as instruments of securitization
or insurance, serving the task of transferring exogenous risk to
capital markets. Illiquidity is a major issue in these markets that calls for an investigation of the micro-economic structure, from which the usual meso-scopic models arise in the context of market equilibria. Dealing with pricing and hedging of these
products, which constitutes the primary mathematical focus of this
project, leads to archetypical models of incomplete financial markets.
The project developed a pivotal stochastic approach of risk
indifference based cross hedging in incomplete finance and insurance
markets by means of quadratic growth Backward Stochastic Differential
Equations (BSDE), founded on the martingale optimality concept and stochastic
calculus of variations. Generalizing the Black-Scholes delta hedge
formula to the incomplete setting, it allows an explicit description of
investment strategies exhibiting the correlation of market and risk in the setting of exponential utility.
A major issue for practical applications
is a numerical analysis of these quadratic growth BSDEs. Our project
presents first results in this direction. We were able to extend
the stochastic calculus of variations to obtain explicit delta hedge
formulas on stochastic bases on which the Brownian motion is replaced
by a continuous Markovian martingale. To develop further the numerical
approach for quadratic growth BSDE (e.g. enhancement of the
convergence
speed), and to extend the cross hedging approach to general utility
functions constitute focal points of future research of the project.
For publications, talks and further information please see the homepages of the project members and E2.
Last Update: 28.12.2009
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