On backward stochastic differential equations approach to valuation of American options
Abstract
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 weak solution to some semilinear partial differential equation.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2010
- DOI:
- 10.48550/arXiv.1012.4442
- arXiv:
- arXiv:1012.4442
- Bibcode:
- 2010arXiv1012.4442K
- Keywords:
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- Mathematics - Probability;
- Mathematics - Analysis of PDEs;
- Mathematics - Optimization and Control
- E-Print:
- Bull. Polish Acad. Sci. Math. 59 (2011) 275-288