Annuncio di Seminario
Luciano Campi, London School of Economics, London
Giovedi' 3 Luglio, presso il Dipartimento di Informatica, Università di
Verona
Strada le Grazie, 15 - Sala Verde
ore 15:00 (14:45 rinfresco, 15:00 inizio seminario)
Title: Utility indifference valuation for non-smooth payoffs with an
application to power derivatives
Abstract: We consider the problem of exponential utility indifference
valuation under the simplified framework where traded and nontraded assets
are uncorrelated but where the claim to be priced possibly depends on both.
Traded asset prices follow a multivariate Black and Scholes model, while
nontraded asset prices evolve as generalized Ornstein-Uhlenbeck processes.
We provide a BSDE characterization of the utility indifference price (UIP)
for a large class of non-smooth, possibly unbounded, payoffs depending
simultaneously on both classes of assets. Focusing then on European claims
and using the Gaussian structure of the model allows us to employ some BSDE
techniques (in particular, a Malliavin-type representation theorem due to
Ma (2002)) to prove the regularity of Z and to characterize the UIP for
possibly discontinuous European payoffs as a viscosity solution of a
suitable PDE with continuous space derivatives. The optimal hedging
strategy is also identified essentially as the delta hedging strategy
corresponding to the UIP. Since there are no closed-form formulas in
general, we also obtain asymptotic expansions for prices and hedging
strategies when the risk aversion parameter is small. Finally, our results
are applied to pricing and hedging power derivatives in various structural
models for energy markets.
Contact Person: Luca Di Persio
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Luca Di Persio - PhD
assistant professor of
Probability and Mathematical Finance
Dept. Informatics University of Verona
strada le Grazie 15 - 37134 Verona - Italy
Tel : +39 045 802 7968
Dept. Math University of Trento
V. Sommarive, 14 - 38123 Povo - Italy
Tel : +39 0461 281686