The infinite dimensional Henstock integral and problems of black-scholes expectation

• Autorzy: Muldowney P.
• Języki publikacji: EN

Abstrakty

EN

Using arguments which apply equally well to the study of Brownian motion and Feynman parth integrals, the relationship between two expressions which arise in derivative asset pricing theory is examined. Detailed explanations are given for some of the key points in the theory of Henstock integrals in function spaces.

Słowa kluczowe

EN

geometric Brownian motion; Feynman path integrals

PL

geometryczny ruch Browniana; ścieżka całki Feynman`a

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2002
• Tom: Vol. 8, nr 1
• Strony: 1--21
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Muldowney P.

• Magee College University of Ulster Northland Road Derry BT48 7JL Northern Ireland,

Bibliografia

• [1] Elliott, R. J., Kopp, P. E., Mathematics of Financial Markets, Springer-Verlag, New York, 1999.
• [2] Henstock, R., Linear Analysis, Butterworths, London, 1968.
• [3] Henstock, R., Integration in product spaces, including Wiener and Feynman integration, Proc. London Math. Soc. 27 (1973), 317-344.
• [4] Henstock, R., The General Theory of Integration, Clarendon Press, Oxford, 1991.
• [5] Henstock, R., The construction of path integrals, Math. Japon. 39(1) (1994), 15-18.
• [6] Kwok, Y. K., Mathematical Models of Financial Derivatives, Springer, Singapore, 1998.
• [7] Muldowney, P., A General Theory of Integration in Function Spaces, Pitman Res. Notes Math. Ser. 153, Longman, Harlow, 1987.
• [8] Muldowney, P., Introduction to Feynman integration, J. Math. Study 27(1) (1994), 127-132.
• [9] Muldowney, P., Topics in probability using generalised Riemann integration, Proc. Royal Irish Acad. Sect. A 99(1) (1999), 39-50.
• [10] Muldowney, R, Feynman’s path integrals and Henstock’s non-absolute integration, J. Appl. Anal. 6(1) (2000), 1-24.
• [11] Muldowney, P., The Henstock integral and the Black-Scholes theory of derivative asset pricing, Real Anal. Exchange 26(1) (2000-2001), 117-132.