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Zapiski Nauchnykh Seminarov POMI, 2009, Volume 368, Pages 20–52 (Mi znsl3501)  
Probabilistic approach to solution of nonlinear PDEs arising in financial mathematics

Ya. I. Belopolskaya

St. Petersburg State University of Architecture and Civil Engineering, St. Petersburg
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Abstract: We apply a probabilistic approach that allows to solve the Cauchy problem for nonlinear parabolic equations and systems developed in our previous papers to problems arising in financial mathematics while constructing arbitrage-free option prices on non-ideal markets. Bibl. – 11 titles.
Key words and phrases: stochastic equations, diffusion processes, nonlinear PDE and systems, contigent claim prices, transaction costs, illiquidity.
Received: 05.11.2009
English version:
Journal of Mathematical Sciences (New York), 2010, Volume 167, Issue 4, Pages 444–460
DOI: https://doi.org/10.1007/s10958-010-9930-0
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
Citation: Ya. I. Belopolskaya, “Probabilistic approach to solution of nonlinear PDEs arising in financial mathematics”, Probability and statistics. Part 15, Zap. Nauchn. Sem. POMI, 368, POMI, St. Petersburg, 2009, 20–52; J. Math. Sci. (N. Y.), 167:4 (2010), 444–460
Citation in format AMSBIB
\Bibitem{Bel09}
\by Ya.~I.~Belopolskaya
\paper Probabilistic approach to solution of nonlinear PDEs arising in financial mathematics
\inbook Probability and statistics. Part~15
\serial Zap. Nauchn. Sem. POMI
\yr 2009
\vol 368
\pages 20--52
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3501}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 167
\issue 4
\pages 444--460
\crossref{https://doi.org/10.1007/s10958-010-9930-0}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77953915368}
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