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Some mathematical results in the pricing of American options. (English) Zbl 0797.60051

The authors elaborate on the problem of pricing an American call option, i.e. the right to buy an asset for a prescribed price at any time up to the expiry date. It is known that this problem requires the solution of a free boundary problem for an associated PDE if the asset price is modelled as a suitable stochastic differential equation. Apart from deriving the equivalence of the pricing and free boundary problems, the authors examine the large- and small-time behaviour, reformulate the problem as a variational inequality, address the question of numerical solution and emphasize the relationship with certain physically motivated free boundary problems.

MSC:

60H30 Applications of stochastic analysis (to PDEs, etc.)
91G20 Derivative securities (option pricing, hedging, etc.)
35K20 Initial-boundary value problems for second-order parabolic equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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References:

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