Elementary stochastic calculus for finance with infinitesimals
Commentationes Mathematicae Universitatis Carolinae (2017)
- Volume: 58, Issue: 1, page 101-124
- ISSN: 0010-2628
Access Full Article
topAbstract
topHow to cite
topReferences
top- Albeverio S., Fenstad J.E., Hoegh-Krohn R., Lindstrom T., Nonstadard Methods in Stochastic Analysis and Mathematical Physics, Dover Publications, 1986. MR0859372
- Anderson R.M., 10.1007/BF02756559, Israel Math. J. 25 (1976), 15–46. Zbl0327.60039MR0464380DOI10.1007/BF02756559
- Bacheier L., La Theorie de la Speculation, Annales de l'Ecole Normale Superieure, 3, Gauthier-Villars, Paris, 1900. MR1508978
- Berg I., Principles of Infinitesimal Stochastic and Financial Analysis, World Scientific, Singapore, 2000. Zbl0964.91024MR1789967
- Brown R., 10.1080/14786442808674769, Phil. Mag. 4 (1828), 161–173. DOI10.1080/14786442808674769
- Cox J., Ross S., Rubinstein M., 10.1016/0304-405X(79)90015-1, J. Financial Econom. 7 (1979), 229–263. Zbl1131.91333DOI10.1016/0304-405X(79)90015-1
- Cutland N., Kopp E., Willinger W., 10.1111/j.1467-9965.1991.tb00017.x, Mathematical Finance 1 (1991), no. 4, 1–38. Zbl0900.90104DOI10.1111/j.1467-9965.1991.tb00017.x
- Cutland N., Kopp E., Willinger W., 10.1080/17442509308833813, Stochastics Stochastics Rep. 42 (1993), 115–133. Zbl0808.90018MR1275815DOI10.1080/17442509308833813
- Cutland N., Kopp E., Willinger W., 10.1080/17442509508833970, Stochastics Stochastics Rep. 52 (1995), 173–192. Zbl0864.60039MR1381667DOI10.1080/17442509508833970
- Cutland N., Kopp E., Willinger W., Wyman M.C., Convergence of Snell envelopess and critical prices in the American put, Mathematics of Derivative Securitities (M.A.H. Dempster and S.R. Pliska, eds.), Cambridge University Press, Cambridge, 1997, pp. 126–140. MR1491372
- Cutland N., 10.1007/b76881, Lecture Notes in Mathematics, 1751, Springer, Berlin, 2000. Zbl0963.28015MR1810844DOI10.1007/b76881
- Einstein A., Investigations on the theory of the Brownian movement, R. Fürth (Ed.), Dover Publications, New York, 1956. Zbl0936.01034MR0077443
- Herzberg F.S., Stochastic Calculus with Infinitesimals, Springer, Heidelberg, 2013. Zbl1302.60006MR2986409
- Hull J., Options, Futures, and Other Derivatives, 8th edition, Prentice Hall, 2011. Zbl1087.91025
- Hurd A.E., Loeb P.A., An Introduction to Nonstandard Real Analysis, Academic Press, Orlando, FL, 1985. Zbl0583.26006MR0806135
- Kalina M., Probability in the alternative set theory, Comment. Math. Univ. Carolin. 30 (1989), no. 2, 347–356. Zbl0677.03039MR1014134
- Keisler J.H., An infinitesimal approach to stochastic analysis, Mem. Amer. Math. Soc. 297, 1984. Zbl0529.60062MR0732752
- Keisler J.H., Elementary Calculus - an Infinitesimal Approach, 2nd edition, University of Wisconsin - Creative Commons., 2000. Zbl0655.26002
- Kopp P.E., Hyperfinite Mathematical Finance, in Arkeryd et al. Nonstandard Analysis: Theory and Applications, Kluwer, Dordrecht, 1997. Zbl0952.91028MR1603237
- Lindstrom T., 10.1007/s11813-007-0004-7, Logic and Analysis 1 (2008), 91–129. Zbl1156.60035MR2403500DOI10.1007/s11813-007-0004-7
- Loeb P.A., 10.1090/S0002-9947-1975-0390154-8, Trans. Amer. Math. Soc. 211 (1975), 113–122. Zbl0312.28004MR0390154DOI10.1090/S0002-9947-1975-0390154-8
- Nelson A., 10.1090/S0002-9904-1977-14398-X, Bull. Amer. Math. Soc. 83 (1977), no. 6, 1165–1198. Zbl0373.02040MR0469763DOI10.1090/S0002-9904-1977-14398-X
- Nelson E., Radically Elementary Probability Theory, Princeton University Press, Princeton, NJ, 1987. Zbl0651.60001MR0906454
- Pudlák P., Sochor A., 10.2307/2274190, J. Symbolic Logic 49 (1984), 570–585. Zbl0578.03028MR0745386DOI10.2307/2274190
- Rebonato R., Volatility and Correlation: the Perfect Hedger and the Fox, 2nd edition, Wiley, 2004.
- Robinson A., Nonstandard analysis, Proc. Roy. Acad. Amsterdam Ser. A 64 (1961), 432–440. Zbl0424.01031MR0142464
- Shreve S., Stochastic Calculus for Finance II. Continuous Time Models, Springer, New York, 2004. Zbl1068.91041MR2057928
- Shreve S., Stochastic Calculus for Finance I. The Binomial Asset Pricing Model, Springer, New York, 2005. Zbl1068.91040MR2049045
- Vopěnka P., Mathematics in the Alternative Set Theory, Teubner, Leipzig, 1979. MR0581368