Fallacy of the Log Normal Approximation to Optimal Portfolio Decision Making Ove
Fallacy of the Log Normal Approximation to Optimal Portfolio Decision Making Ove
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In our eReader you can find the full English version of the book. Read Fallacy of the Log Normal Approximation to Optimal Portfolio Decision Making Ove Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Fallacy of the Log Normal Approximation to Optimal Portfolio Decision Making Ove
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(T, T;h) ], then from (7. 5), we have that Y. (T;h) S Z X. (k, h) where N = T/h, (7. 17) 3 k=l ^ and from the independence and identical distribution of the X. ( ;h), the moment-generating function of Y. Will satisfy 0. (X;h, T) = E{exp[XY. (T;h)]} (7. 18) Taking logs of both sides of (7. 18) and using Taylor series, we have that log[0^(X;h, T)] = (T/h)log[4^. (X;h)] (7. 19) 00 = (T/h)log[ I t|^/^^(0;h)x'^/k!] k=0 ^ = (T/h)log[ Z m. (k;h)A^/k!] k=0 ^ = (T/h)log[l + m. (l;h)X + l/2m. (2;h)X^ + o...(h) ] = T[X(m. (l;h)/h) + ^(m. (2;h)/h) + 0(h)].
2 2 2 Substituting y (h)h for m. (l;h) and O. (h)h + y, (h)h for m. (2;h) and taking the limit as h^o in (7. 19), we have that log[0. (X;O, T)] = lim log[0(X;h, T) ] (7. 20) J h->0 = Xy. T + l/2a.^TX^, and therefore, 0. (X;O, T) is the moment-generating function for a normally- 2 distributed random variable with mean y. T and variance O. T.
35 Thus, in what is essentially a valid application of the Central- Limit theorem, we have shown that the limit distribution for Y.
What to read after Fallacy of the Log Normal Approximation to Optimal Portfolio Decision Making Ove?
You can find similar books in the "Read Also" column, or choose other free books by Robert C Merton to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
(T, T;h) ], then from (7. 5), we have that Y. (T;h) S Z X. (k, h) where N = T/h, (7. 17) 3 k=l ^ and from the independence and identical distribution of the X. ( ;h), the moment-generating function of Y. Will satisfy 0. (X;h, T) = E{exp[XY. (T;h)]} (7. 18) Taking logs of both sides of (7. 18) and using Taylor series, we have that log[0^(X;h, T)] = (T/h)log[4^. (X;h)] (7. 19) 00 = (T/h)log[ I t|^/^^(0;h)x'^/k!] k=0 ^ = (T/h)log[ Z m. (k;h)A^/k!] k=0 ^ = (T/h)log[l + m. (l;h)X + l/2m. (2;h)X^ + o...(h) ] = T[X(m. (l;h)/h) + ^(m. (2;h)/h) + 0(h)].
2 2 2 Substituting y (h)h for m. (l;h) and O. (h)h + y, (h)h for m. (2;h) and taking the limit as h^o in (7. 19), we have that log[0. (X;O, T)] = lim log[0(X;h, T) ] (7. 20) J h->0 = Xy. T + l/2a.^TX^, and therefore, 0. (X;O, T) is the moment-generating function for a normally- 2 distributed random variable with mean y. T and variance O. T.
35 Thus, in what is essentially a valid application of the Central- Limit theorem, we have shown that the limit distribution for Y.
What to read after Fallacy of the Log Normal Approximation to Optimal Portfolio Decision Making Ove?
You can find similar books in the "Read Also" column, or choose other free books by Robert C Merton to read onlineMoreLess
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