From binomial expectations to the Black-Scholes formula : the main ideas
Annales Mathématiques Blaise Pascal, Tome 4 (1997) no. 1, pp. 93-101.
@article{AMBP_1997__4_1_93_0,
author = {van den Berg, I.P. and Koudjeti, F.},
title = {From binomial expectations to the Black-Scholes formula : the main ideas},
journal = {Annales Math\'ematiques Blaise Pascal},
pages = {93--101},
publisher = {Laboratoires de Math\'ematiques Pures et Appliqu\'ees de l'Universit\'e Blaise Pascal},
volume = {4},
number = {1},
year = {1997},
zbl = {0895.60020},
mrnumber = {1442337},
language = {en},
url = {www.numdam.org/item/AMBP_1997__4_1_93_0/}
}
van den Berg, I. P.; Koudjeti, F. From binomial expectations to the Black-Scholes formula : the main ideas. Annales Mathématiques Blaise Pascal, Tome 4 (1997) no. 1, pp. 93-101. http://www.numdam.org/item/AMBP_1997__4_1_93_0/

[1] R.M. Anderson. A nonstandard representation for brownian motion and itô integration. Israel Math. J., 25:15-46, 1976. | MR 464380 | Zbl 0353.60052

[2] E. Benoit. Random walks and stochastic differential equations. In F.Diener and M. Diener, Nonstandard Analysis in Practice, pages 71-90. Springer Verlag Universitext, 1995. | MR 1396798

[3] I.P. Berg and F. Koudjeti. On binomial expectations and option pricing. SOM, RUG, Groningen, The Netherlands, 95A06, 1995.

[4] F. Black and M. Scholes. The pricing of options and corporate liabilities. Journal of Political Economy, pages 637-654, May-June 1973. | MR 3363443 | Zbl 1092.91524

[5] J.C. Cox, S.A. Ross, and M. Rubinstein. Option pricing: a simplified approach. Journal of Financial Economics, 7:229-263, July 1979. | Zbl 1131.91333

[6] N.G. Cutland, E. Kopp, and W. Willinger. A nonstandard approach to option pricing. Mathematical finance, 1(16):1-38, 1991. | Zbl 0900.90104

[7] F. Diener and G. Reeb. Analyse Non Standard. Enseignement des sciences. Hermann Editeurs, Paris, 1989. | MR 1026099 | Zbl 0682.26010

[8] D. Duffie. Security markets, stochastic models. Economic theory, econometrics and mathematical economics. Academic Press Inc., London, UK, 1988. | MR 955269 | Zbl 0661.90001

[9] J.M. Harrison and S. Pliska. Martingales and stochastic integrals in the theory of continuous trading. Stochastic processes and their applications, 11:215-260, 1981. | MR 622165 | Zbl 0482.60097

[10] F. Koudjeti. Elements of external calculus with an application to mathematical finance. Theses on Systems, Organisations and Management. Capelle a/d IJssel, Labyrint Publication, The Netherlands, June 1995.

[11] F. Koudjeti and I. P. V. D. Berg. Neutrices, external numbers and external calculus. In F. Diener and M. Diener, Nonstandard Analysis in Practice, pages 145-170. Springer Verlag Universitext, 1995. | MR 1396801

[12] P.A. Loeb. Conversion from nonstandard to standard measure spaces and applications in probability theory. Trans. Amer. Math. Soc., 211:113-122,1975. | MR 390154 | Zbl 0312.28004

[13] R. Lutz and M. Goze. Nonstandard analysis: a practical guide with applications, volume 881 of Lecture Notes in Mathematics. Springer verlag, 1981. | MR 643624 | Zbl 0506.03021

[14] E. Nelson. Internal set theory: A new approach to nonstandard analysis. Bulletin of the American Mathematical Society, 83(6):1165-1198, November 1977. | MR 469763 | Zbl 0373.02040

[15] E. Nelson. Radically Elementary Probability Theory, volume 117 of Annals of Mathematical Studies. Princeton University Press, 1987. | MR 906454 | Zbl 0651.60001

[16] A. Robinson. Non-standard Analysis, 2nd edition. North-Holland Pub. Co., 1974. | MR 205854