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Variational inequalities and the pricing of American options. (English) Zbl 0714.90004
Summary: This paper is devoted to the derivation of some regularity properties of pricing functions for American options and to the discussions of numerical methods, based on the Bensoussan-Lions methods of variational inequalities. In particular, we provide a complete justification of the so-called Brennan-Schwartz algorithm for the valuation of American put options.
MSC:
91B28Finance etc. (MSC2000)
60G40Stopping times; optimal stopping problems; gambling theory
49J40Variational methods including variational inequalities
60J60Diffusion processes
65K10Optimization techniques (numerical methods)
65M12Stability and convergence of numerical methods (IVP of PDE)
91B24Price theory and market structure
60H10Stochastic ordinary differential equations
91B62Growth models in economics
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