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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:
91B28 Finance etc. (MSC2000)
60G40 Stopping times; optimal stopping problems; gambling theory
49J40 Variational inequalities
60J60 Diffusion processes
65K10 Numerical optimization and variational techniques
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
91B24 Microeconomic theory (price theory and economic markets)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
91B62 Economic growth models
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