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Stationary solutions for two nonlinear Black–Scholes type equations. (English) Zbl 1063.91026

Summary: We study by topological methods two different problems arising in the Black–Scholes model for option pricing. More specifically, we consider a nonlinear differential equation which generalizes the Black–Scholes formula when the volatility is assumed to be stochastic. On the other hand, we study a model with transaction costs.

MSC:

91B28 Finance etc. (MSC2000)
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[1] Avellaneda, M.; Lawrence, P., Quantitative modeling of derivative securities: from theory to practice, (2000), Chapman & Hall/CRC Boca Raton, FL · Zbl 1058.91529
[2] Avellaneda, M.; Zhu, Y., Risk neutral stochastic volatily model, Internat. J. theor. appl. finance, 1, 2, 289-310, (1998) · Zbl 0909.90036
[3] Duffie, D., Dynamic asset pricing theory, (1996), Princeton University Press Princeton, NJ
[4] Gilbarg, D.; Trudinger, N.S., Elliptic partial differential equations of second order, (1983), Springer Berlin · Zbl 0691.35001
[5] Hull, J.C., Options, futures, and other derivatives, (1997), Prentice-Hall Englewood Cliffs, NJ · Zbl 1087.91025
[6] Ikeda, S., Watanabe, stochastic differential equations and diffusion processes, (1989), North-Holland Amsterdam
[7] Jarrow, R.A., Modelling fixed income securities and interest rate options, (1997), McGraw-Hill New York · Zbl 1079.91532
[8] Merton, R.C., Continuous-time finance, (2000), Blackwell Cambridge
[9] Wilmott, P.; Dewynne, J.; Howison, S., Option pricing, (2000), Oxford Financial Press Oxford
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