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GENERALIZED BROWNIAN MOTIONS WITH APPLICATION TO FINANCE
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 Title & Authors
GENERALIZED BROWNIAN MOTIONS WITH APPLICATION TO FINANCE
Chung, Dong-Myung; Lee, Jeong-Hyun;
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 Abstract
Let be a generalized Brownian motion(gBm) determined by mean function a(t) and variance function b(t). Let denote the Hilbert space of square integrable functionals of . In this paper we consider a class of nonlinear functionals of X of the form F(. + a) with and discuss their analysis. Firstly, it is shown that such functionals do not enjoy, in general, the square integrability and Malliavin differentiability. Secondly, we establish regularity conditions on F for which F(.+ a) is in and has its Malliavin derivative. Finally we apply these results to compute the price and the hedging portfolio of a contingent claim in our financial market model based on a gBm X.ഀĀ᐀會Ā᐀ﶖ⨀㡚�瀀ꀏ會Ā䁇ﶖ⨀⎞ऀĀ᐀會Ā᐀顇ﶖ⨀烛�Ā㰀會Ā㰀ﶖ⨀ࣜ�Ā㈀會Ā㈀䡈ﶖ⨀ꃜ�Ā᐀會Ā᐀ꁈﶖ⨀㣝�Ā᐀會Ā᐀ﶖ⨀택�Ā저會Ā저偉ﶖ⨀颵⎞ऀĀ저會Ā저ꡉﶖ⨀ザ⎞ഀĀ저會Ā저Jﶖ⨀좶⎞Ā저會Ā저塊ﶖ⨀࡙�؀Ā؀會Ā؀끊ﶖ⨀ꁙ�䬀Ā切會Ā切ࡋﶖ⨀µ⎞Ā搀會Ā搀恋ﶖ⨀䠤璮Ā저會Ā저롋ﶖ⨀ႛ蒥Ā저會Ā저၌ﶖ⨀耢璮ࠀĀࠀ會Āࠀ桌ﶖ⨀ᠣ璮Ā저會Ā저쁌ﶖ⨀뀣璮ጀĀ저會Ā저ᡍﶖ⨀ꢛ蒥
 Keywords
generalized Brownian motion;Malliavin derivative;Black-Scholes model;Hedging portfolio;
 Language
English
 Cited by
1.
Effect of drift of the generalized Brownian motion process: an example for the analytic Feynman integral, Archiv der Mathematik, 2016, 106, 6, 591  crossref(new windwow)
2.
A TRANSLATION THEOREM FOR THE GENERALIZED FOURIER-FEYNMAN TRANSFORM ASSOCIATED WITH GAUSSIAN PROCESS ON FUNCTION SPACE, Journal of the Korean Mathematical Society, 2016, 53, 5, 991  crossref(new windwow)
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