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Regularity of the free boundary for the American put option
| 1. | Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260 |
| 2. | Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada |
References:
| [1] |
E. Bayraktar and H. Xing, Analysis of the optimal exercise boundary of American option for jump diffusions, SIAM. J. Math. Anal., 41 (2009), 825-860.
doi: 10.1137/080712519. |
| [2] |
A. Bensoussan, On the theory of option pricing, Acta Appl. Math., 2 (1984), 139-158. |
| [3] |
A. Bensoussan & J.-L. Lions, "Application of Variational Inequalities in Stochastic Control," Studies in Mathematics and its Applications, 12, North-Holland Publishing Co., Amsterdam-New York, 1982. |
| [4] |
X. Chen and J. Chadam, A mathematical analysis of the optimal boundary for American put options, SIAM J. Math. Anal., 38 (2006/07), 1613-1641. |
| [5] |
Xinfu Chen and J. Chadam, Analytic and numerical approximations for the early exercise boundary for American put options, Dyn. Cont. Disc. and Impulsive Sys., 10 (2003), 649-657. |
| [6] |
Xinfu Chen, J. Chadam and Huibin Cheng, Non-convexity of the optimal exercise boundary for an American put option on a dividend-paying asset, Mathematical Finance, to appear. Available from: http://www.pitt.edu/~chadam/papers/LargeDNonConvex.pdf. |
| [7] |
Xinfu Chen, J. Chadam, L. Jiang and W. Zheng, Convexity of the exercise boundary of the American put option on a zero dividend asset, Math. Finance, 18 (2008), 185-197.
doi: 10.1111/j.1467-9965.2007.00328.x. |
| [8] |
A. Friedman, "Variational Principles and Free Boundary Problems," A Wiley-Interscience Publication, Pure and Applied Mathematics, John Wiley & Sons, Inc., New York, 1982. |
| [9] |
A. Friedman, "Partial Diffferential Equations of Parabolic Type," Prentice-Hall, 1964. |
| [10] |
A. Friedman, Analyticity of the free boundary for the Stefan problem, Arch. Rational Mech. Anal., 61 (1976), 97-125.
doi: 10.1007/BF00249700. |
| [11] |
L. Jiang, Existence and differentiability of the solution of a two phase Stefan problem for quasi-linear parabolic equations, Chinese Math. Acta, 7 (1965), 481-496. |
| [12] |
D. Lamberton and M. Mikou, The critical price for the American put in an exponential Lévy model, Finance Stoch., 12 (2008), 561-581.
doi: 10.1007/s00780-008-0073-9. |
| [13] |
P. Laurence and S. Salsa, Regularity of the free boundary of an American option on several assets, Comm. on Pure and Appl. Math., 62 (2009), 969-994.
doi: 10.1002/cpa.20268. |
| [14] |
H. P. McKean, Jr., Appendix: A free boundary problem for the heat equation arising from a problem in mathematical economics, Industrial Management Review, 6 (1965), 32-39. |
| [15] |
P. van Moerbeke, On optimal stopping and free boundary problems, Arch. Rational Mech. Anal., 60 (1975/76), 101-148. |
| [16] |
C. Yang, L. Jiang and B. Bian, Free boundary and American option in a jump-diffusion model, Euro. J. of Applied Mathematics, 17 (2006), 95-127.
doi: 10.1017/S0956792505006340. |
| [17] |
P. Wilmott, J. Dewynne and S. Howison, "The Mathematics of Financial Derivatives. A Student Introduction," Cambridge University Press, Cambridge, 1995. |
show all references
References:
| [1] |
E. Bayraktar and H. Xing, Analysis of the optimal exercise boundary of American option for jump diffusions, SIAM. J. Math. Anal., 41 (2009), 825-860.
doi: 10.1137/080712519. |
| [2] |
A. Bensoussan, On the theory of option pricing, Acta Appl. Math., 2 (1984), 139-158. |
| [3] |
A. Bensoussan & J.-L. Lions, "Application of Variational Inequalities in Stochastic Control," Studies in Mathematics and its Applications, 12, North-Holland Publishing Co., Amsterdam-New York, 1982. |
| [4] |
X. Chen and J. Chadam, A mathematical analysis of the optimal boundary for American put options, SIAM J. Math. Anal., 38 (2006/07), 1613-1641. |
| [5] |
Xinfu Chen and J. Chadam, Analytic and numerical approximations for the early exercise boundary for American put options, Dyn. Cont. Disc. and Impulsive Sys., 10 (2003), 649-657. |
| [6] |
Xinfu Chen, J. Chadam and Huibin Cheng, Non-convexity of the optimal exercise boundary for an American put option on a dividend-paying asset, Mathematical Finance, to appear. Available from: http://www.pitt.edu/~chadam/papers/LargeDNonConvex.pdf. |
| [7] |
Xinfu Chen, J. Chadam, L. Jiang and W. Zheng, Convexity of the exercise boundary of the American put option on a zero dividend asset, Math. Finance, 18 (2008), 185-197.
doi: 10.1111/j.1467-9965.2007.00328.x. |
| [8] |
A. Friedman, "Variational Principles and Free Boundary Problems," A Wiley-Interscience Publication, Pure and Applied Mathematics, John Wiley & Sons, Inc., New York, 1982. |
| [9] |
A. Friedman, "Partial Diffferential Equations of Parabolic Type," Prentice-Hall, 1964. |
| [10] |
A. Friedman, Analyticity of the free boundary for the Stefan problem, Arch. Rational Mech. Anal., 61 (1976), 97-125.
doi: 10.1007/BF00249700. |
| [11] |
L. Jiang, Existence and differentiability of the solution of a two phase Stefan problem for quasi-linear parabolic equations, Chinese Math. Acta, 7 (1965), 481-496. |
| [12] |
D. Lamberton and M. Mikou, The critical price for the American put in an exponential Lévy model, Finance Stoch., 12 (2008), 561-581.
doi: 10.1007/s00780-008-0073-9. |
| [13] |
P. Laurence and S. Salsa, Regularity of the free boundary of an American option on several assets, Comm. on Pure and Appl. Math., 62 (2009), 969-994.
doi: 10.1002/cpa.20268. |
| [14] |
H. P. McKean, Jr., Appendix: A free boundary problem for the heat equation arising from a problem in mathematical economics, Industrial Management Review, 6 (1965), 32-39. |
| [15] |
P. van Moerbeke, On optimal stopping and free boundary problems, Arch. Rational Mech. Anal., 60 (1975/76), 101-148. |
| [16] |
C. Yang, L. Jiang and B. Bian, Free boundary and American option in a jump-diffusion model, Euro. J. of Applied Mathematics, 17 (2006), 95-127.
doi: 10.1017/S0956792505006340. |
| [17] |
P. Wilmott, J. Dewynne and S. Howison, "The Mathematics of Financial Derivatives. A Student Introduction," Cambridge University Press, Cambridge, 1995. |
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