Dynamic Technical Analysis by Philippe Cahen
By Philippe Cahen
I do not like booklet translations, so i purchased this booklet at Amazon.France, french language. I't an outstanding better half to John Bollinger e-book. This paintings gains attention-grabbing visible process, with reviews of slopes and shapes of bollinger bands.
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Additional resources for Dynamic Technical Analysis
Example text
4) simply by defining a new BDLP z˜ = {˜z, t 0} by z˜ t = zt + λ−1 αt. e. there The process y = {yt , t exists a law D, called the stationary law or the marginal law, such that yt will follow the law D for every t if the initial y0 is chosen according to D. The process y moves up entirely by jumps and then tails off exponentially. In Barndorff-Nielsen and Shephard (2001a) some stochastic properties of y are studied. They established the notation that if y is an OU process with marginal law D, then we say that y is a D-OU process.
1). 46 LÉVY PROCESSES Predictable Representation Property We denote the jump that a process X = {Xt , t 0} makes at time t by Xt = Xt − Xt− . Under some weak moment assumptions it was proved in Nualart and Schoutens (2000) t T } possesses a version of the predictable that a Lévy process X = {Xt , 0 representation property (PRP). e. 2) s T } is the i = 2, 3, . . ( X u )i , 0
0 A major feature of the intOU process Y is Yt = λ−1 (zλt − yt + y0 ) t = λ−1 (1 − exp(−λt))y0 + λ−1 (1 − exp(−λ(t − s))) dzλs . 6) 0 An interesting characteristic is that Y = {Yt , t when λ > 0, while z = {zt , t 0} and y = {yt , t 0} has continuous sample paths 0} have jumps. 50 EXAMPLES OF LÉVY PROCESSES We can show (see Barndorff-Nielsen and Shephard 2001a) that, given y0 , log E[exp(iuYt ) | y0 ] t =λ k(uλ−1 (1 − exp(−λ(t − s)))) ds + iuy0 λ−1 (1 − exp(−λt)), 0 where k(u) = kz (u) = log E[exp(−uz1 )] is the cumulant function of z1 .