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)

Abstract:

*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.