An Introduction to Algorithmic Finance, Algorithmic Trading and Blockchain by Satya Chakravarty;Palash Sarkar;
Author:Satya Chakravarty;Palash Sarkar; [Неизв.]
Language: eng
Format: epub
ISBN: 9781789738957
Publisher: Emerald Publishing
Published: 2019-09-24T21:00:00+00:00
be the set all possible portfolios over n assets A 1,â¦,A n . Note that, in this formulation we do not consider negative weights. We consider T time periods. The price relative for A i in time period t will be denoted as r t,i , t = 1,â¦,T and i = 1,â¦,n. The price relative for all the assets in time period t will be denoted as r t = (r t,1,â¦,r t,n ). The sequence of price relatives r 1,â¦,r t will be denoted as r (t).
Given a portfolio p, by CRP p we will denote the CRP strategy executed with portfolio p, i.e. after each period, the wealth is re-distributed among the assets according to the portfolio p. Fix a portfolio . Given the initial wealth to be X 0, after the first time period the wealth becomes , where (p·r 1) denotes the dot product of p and r 1 and is equal to . By a similar reasoning, the wealth at the end of second period is X 2 = X 1(p·r 2) = X 0(p·r 1)(p·r 2). Extending, we have that the wealth at the end of t time periods is X t = X 0(p·r 1)â¯(p·r t ). The growth in wealth is X t /X 0 and we define
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