Venerdì 23 Febbraio alle ore 14:00, in aula 3014 del Dipartimento di
Matematica e Applicazioni (edificio U5, via Cozzi 55, Milano), Università
di Milano-Bicocca,
il Prof. Francesco Russo (ENSTA ParisTech)
terrà un seminario dal titolo
"BSDEs, martingale problems, associated deterministic equations and
applications to finance"
*Abstract:* The aim of this talk consists in introducing a new formalism
for the deterministic analysis associated with backward stochastic
differential equations driven by general càdlàg martingales,
coupled with a forward Markov process.
When the martingale is a standard Brownian motion, the natural
deterministic analysis is provided by the solution u of a semilinear PDE of
parabolic type coupled with a function v which is associated with the ∇u,
when u is of class C^1 in space. When u is only a viscosity solution of the
PDE, the link associating v to u is not completely clear: sometimes in the
literature it is called the identification problem.
The idea is to introduce a suitable analysis to investigate the equivalent
of the identification problem in a general Markovian setting with a class
of examples. An interesting application concerns the hedging problem under
basis risk of a contingent claim g(X(T),S(T) ), where S (resp. X) is an
underlying price of a traded (resp. non-traded but observable) asset, via
the celebrated Föllmer-Schweizer decomposition. We revisit the case when
the couple of price processes (X, S) is a diffusion and we provide explicit
expressions when (X, S) is an exponential of additive processes.
Tutti gli interessati sono invitati a partecipare.
Cordialmente,
Federica Masiero