Geodesic
Probabilistic approach to a~free boundary problem and American option procing
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 16, Tome 384 (2010), pp. 40-77

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In this paper we discuss a probabilistic approach to the construction of a solution of a free boundary problem for parabolic and integro-differential equations which is associated with an optimization problem for a stochastic equation with diffusion and jumps. The results are applied to calculation of American option prices in Black–Scholes and Merton models. Bibl. 22 titles. 
@article{ZNSL_2010_384_a3,
     author = {Ya. I. Belopolskaya and M. M. Romadanova},
     title = {Probabilistic approach to a~free boundary problem and {American} option procing},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {40--77},
     publisher = {mathdoc},
     volume = {384},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_384_a3/}
}
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Ya. I. Belopolskaya; M. M. Romadanova. Probabilistic approach to a~free boundary problem and American option procing. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 16, Tome 384 (2010), pp. 40-77. http://geodesic.mathdoc.fr/item/ZNSL_2010_384_a3/