backward stochastic differential equations
reflected stochastic differential equations
Reflected forward backward stochastic differential equations and contingent claims
The theory of stochastic differential equations was originally developed as a tool for the explicit construction of the trajectories of a diffusion process for given coefficients of drift and diffusion, on the other hand, stochastic differential equations arise in the description of systems on which so called ``white noise'' acts. In this paper the author gives an application of stochastic differential equations in economic (The theory of pricing contingent claims). The author defined the basis of a trivial control problem and that the formal adjoint process of this control problem is given by BSDE (backward stochastic differential equations). The author defined also the stochastic pricing system for the claim, and he explained that BSDE is a tool to model evalutions of the claims. In order to determine the pricing of the claim it is necessary to solve the BSDE. Finally the American contigent claim is studied and the main results of pricing of the American claim is given in theorem 2 which is a solution of a reflected backward Stochastic differential equation. I think that the results in theorem 2 is interesting for applications.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00050].
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