American Institute of Mathematical Sciences

Advanced
September  2006, 5(3): 505-514. doi: 10.3934/cpaa.2006.5.505

A boundary point lemma for Black-Scholes type operators

Erik Ekström 1, and  Johan Tysk 2,

1. 

School of Mathematics, The University of Manchester, Sackville Street, Manchester M60 1QD, United Kingdom
2. 

Department of Mathematics, Uppsala University, P.O. Box 480, SE-75106 Uppsala, Sweden

Received  May 2005 Revised  January 2006 Published  June 2006

We prove a sharp version of the Hopf boundary point lemma for Black-Scholes type equations. We also investigate the existence and the regularity of the spatial derivative of the solutions at the spatial boundary.
Keywords: degenerate equations, Black-Scholes equation., Hopf boundary point lemma, parabolic equations.
Mathematics Subject Classification: Primary: 35K65, 35B50; Secondary: 91B2.
Citation: Erik Ekström, Johan Tysk. A boundary point lemma for Black-Scholes type operators. Communications on Pure & Applied Analysis, 2006, 5 (3) : 505-514. doi: 10.3934/cpaa.2006.5.505
[1]

Junkee Jeon, Jehan Oh. (1+2)-dimensional Black-Scholes equations with mixed boundary conditions. Communications on Pure & Applied Analysis, 2020, 19 (2) : 699-714. doi: 10.3934/cpaa.2020032
[2]

Marjan Uddin, Hazrat Ali. Space-time kernel based numerical method for generalized Black-Scholes equation. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020221
[3]

Kais Hamza, Fima C. Klebaner. On nonexistence of non-constant volatility in the Black-Scholes formula. Discrete & Continuous Dynamical Systems - B, 2006, 6 (4) : 829-834. doi: 10.3934/dcdsb.2006.6.829
[4]

Rehana Naz, Imran Naeem. Exact solutions of a Black-Scholes model with time-dependent parameters by utilizing potential symmetries. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020122
[5]

Rodrigue Gnitchogna Batogna, Abdon Atangana. Generalised class of Time Fractional Black Scholes equation and numerical analysis. Discrete & Continuous Dynamical Systems - S, 2019, 12 (3) : 435-445. doi: 10.3934/dcdss.2019028
[6]

Piermarco Cannarsa, Patrick Martinez, Judith Vancostenoble. The cost of controlling weakly degenerate parabolic equations by boundary controls. Mathematical Control & Related Fields, 2017, 7 (2) : 171-211. doi: 10.3934/mcrf.2017006
[7]

Hiroshi Watanabe. Solvability of boundary value problems for strongly degenerate parabolic equations with discontinuous coefficients. Discrete & Continuous Dynamical Systems - S, 2014, 7 (1) : 177-189. doi: 10.3934/dcdss.2014.7.177
[8]

Chunlai Mu, Zhaoyin Xiang. Blowup behaviors for degenerate parabolic equations coupled via nonlinear boundary flux. Communications on Pure & Applied Analysis, 2007, 6 (2) : 487-503. doi: 10.3934/cpaa.2007.6.487
[9]

Raluca Clendenen, Gisèle Ruiz Goldstein, Jerome A. Goldstein. Degenerate flux for dynamic boundary conditions in parabolic and hyperbolic equations. Discrete & Continuous Dynamical Systems - S, 2016, 9 (3) : 651-660. doi: 10.3934/dcdss.2016019
[10]

Toshi Ogawa. Degenerate Hopf instability in oscillatory reaction-diffusion equations. Conference Publications, 2007, 2007 (Special) : 784-793. doi: 10.3934/proc.2007.2007.784
[11]

Lingyu Jin, Yan Li. A Hopf's lemma and the boundary regularity for the fractional p-Laplacian. Discrete & Continuous Dynamical Systems - A, 2019, 39 (3) : 1477-1495. doi: 10.3934/dcds.2019063
[12]

Takesi Fukao, Masahiro Kubo. Nonlinear degenerate parabolic equations for a thermohydraulic model. Conference Publications, 2007, 2007 (Special) : 399-408. doi: 10.3934/proc.2007.2007.399
[13]

Young-Sam Kwon. Strong traces for degenerate parabolic-hyperbolic equations. Discrete & Continuous Dynamical Systems - A, 2009, 25 (4) : 1275-1286. doi: 10.3934/dcds.2009.25.1275
[14]

Jiebao Sun, Boying Wu, Jing Li, Dazhi Zhang. A class of doubly degenerate parabolic equations with periodic sources. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 1199-1210. doi: 10.3934/dcdsb.2010.14.1199
[15]

Morteza Fotouhi, Leila Salimi. Controllability results for a class of one dimensional degenerate/singular parabolic equations. Communications on Pure & Applied Analysis, 2013, 12 (3) : 1415-1430. doi: 10.3934/cpaa.2013.12.1415
[16]

Hiroshi Watanabe. Existence and uniqueness of entropy solutions to strongly degenerate parabolic equations with discontinuous coefficients. Conference Publications, 2013, 2013 (special) : 781-790. doi: 10.3934/proc.2013.2013.781
[17]

Piermarco Cannarsa, Patrick Martinez, Judith Vancostenoble. Persistent regional null contrillability for a class of degenerate parabolic equations. Communications on Pure & Applied Analysis, 2004, 3 (4) : 607-635. doi: 10.3934/cpaa.2004.3.607
[18]

Kristian Bredies. Weak solutions of linear degenerate parabolic equations and an application in image processing. Communications on Pure & Applied Analysis, 2009, 8 (4) : 1203-1229. doi: 10.3934/cpaa.2009.8.1203
[19]

Giuseppe Floridia. Well-posedness for a class of nonlinear degenerate parabolic equations. Conference Publications, 2015, 2015 (special) : 455-463. doi: 10.3934/proc.2015.0455
[20]

Hongtao Li, Shan Ma, Chengkui Zhong. Long-time behavior for a class of degenerate parabolic equations. Discrete & Continuous Dynamical Systems - A, 2014, 34 (7) : 2873-2892. doi: 10.3934/dcds.2014.34.2873

2018 Impact Factor: 0.925

Tools

Metrics

  • PDF downloads (36)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences