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On Backward Stochastic Differential Equations Approach to Valuation of American Options

Klimsiak T., Rozkosz A.

Bulletin of the Polish Academy of Sciences. Mathematics

2011

Vol. 59, no 3

275--288

We consider the problem of valuation of American (call and put) options written on a dividend paying stock governed by the geometric Brownian motion. We show that the value function has two different but related representations: by means of a solution of some nonlinear backward stochastic differential equation, and by a weak solution to some semilinear partial differential equation.