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Remarks on the pricing of contingent claims under constraints

Bensoussan, Alain (2004), Remarks on the pricing of contingent claims under constraints, IEEE Transactions on Automatic Control, 49, 3, p. 433-441. http://dx.doi.org/10.1109/TAC.2004.824475

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Type
Article accepté pour publication ou publié
Date
2004
Journal name
IEEE Transactions on Automatic Control
Volume
49
Number
3
Publisher
IEEE
Pages
433-441
Publication identifier
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Author(s)
Bensoussan, Alain
Abstract (EN)
The study of the pricing of contingent claims under constraints leads, in the case of stocks obeying lognormal distributions, to an interesting analytical result. Namely, the price satisfies the Black Scholes equation with a different initial condition. We give a mostly analytical treatment of this result, using the probabilistic interpretation of the Cauchy problem, with nonsmooth initial conditions.
Subjects / Keywords
Cauchy problem; Black Scholes equation