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NCTS-Sinica Probability Seminar
14:20 - 15:10, April 15, 2019 (Monday)
R202, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 202室)
Backward Stochastic Differential Equations, Martingale Problems, Associated Deterministic Equations and Applications to Hedging under Basis Risk (Mathematical Finance)
Francesco Russo (ENSTA Paris Tech)


The talk will be based on partial joint work with  Adrien Barrasso (ENSTA ParisTech) and Ismail Laachir (ZELIADE).
The aim of this talk consists in introducing a new formalism for the deterministic analysis  associated with backward stochastic differential equations  driven by general  martingales, coupled with a forward  process.
When the martingale is a standard Brownian motion, the natural deterministic analysis is provided by the solution of a semilinear PDE of parabolic type coupled with a function which is associated with the  , when is of class in space. When is only a viscosity solution of the PDE, the link associating to 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 , where (resp. ) 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 is a diffusion and we provide explicit expressions when is an exponential of additive processes. Extensions to non-Markovian (path-dependent cases) are discussed.


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