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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.
91B28Finance etc. (MSC2000)
Full Text: DOI
[1] Avellaneda, M.; Lawrence, P.: Quantitative modeling of derivative securities: from theory to practice. (2000) · Zbl 1058.91529
[2] Avellaneda, M.; Zhu, Y.: Risk neutral stochastic volatily model. Internat. J. Theor. appl. Finance 1, No. 2, 289-310 (1998) · Zbl 0909.90036
[3] Duffie, D.: Dynamic asset pricing theory. (1996) · Zbl 1140.91041
[4] Gilbarg, D.; Trudinger, N. S.: Elliptic partial differential equations of second order. (1983) · Zbl 0562.35001
[5] Hull, J. C.: Options, futures, and other derivatives. (1997) · Zbl 1087.91025
[6] Ikeda, S.: Watanabe, stochastic differential equations and diffusion processes. (1989) · Zbl 0684.60040
[7] Jarrow, R. A.: Modelling fixed income securities and interest rate options. (1997) · Zbl 1079.91532
[8] Merton, R. C.: Continuous-time finance. (2000) · Zbl 1019.91502
[9] Wilmott, P.; Dewynne, J.; Howison, S.: Option pricing. (2000) · Zbl 0844.90011