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Zapiski Nauchnykh Seminarov POMI, 2010, Volume 384, Pages 40–77 (Mi znsl3885)  
Probabilistic approach to a free boundary problem and American option procing

Ya. I. Belopolskaya, M. M. Romadanova

St. Petersburg State University of Architecture and Civil Engineering, Saint Petersburg
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Abstract: 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.
Key words and phrases: free boundary, diffusion process, Lévy process, parabolic and integro-differential equations, American option.
Received: 03.11.2010
English version:
Journal of Mathematical Sciences (New York), 2011, Volume 176, Issue 2, Pages 124–145
DOI: https://doi.org/10.1007/s10958-011-0406-7
Bibliographic databases:
Document Type: Article
UDC: 519
Language: Russian
Citation: Ya. I. Belopolskaya, M. M. Romadanova, “Probabilistic approach to a free boundary problem and American option procing”, Probability and statistics. Part 16, Zap. Nauchn. Sem. POMI, 384, POMI, St. Petersburg, 2010, 40–77; J. Math. Sci. (N. Y.), 176:2 (2011), 124–145
Citation in format AMSBIB
\Bibitem{BelRom10}
\by Ya.~I.~Belopolskaya, M.~M.~Romadanova
\paper Probabilistic approach to a~free boundary problem and American option procing
\inbook Probability and statistics. Part~16
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 384
\pages 40--77
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3885}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2011
\vol 176
\issue 2
\pages 124--145
\crossref{https://doi.org/10.1007/s10958-011-0406-7}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79959568880}
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