STAC70H3 Lecture Notes - Borel Set, Countable Set, Sigma-Algebra
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Return: change in price of an asset as a proportion of the initial price. Note: pt/pt-k = pt/pt-1 x pt-1/pt-2 pt-k+1/pt-k = (1+rt)(1+rt-1)(1+rt-k+1) Def: rt = ln (pt/pt-1) = ln pt ln pt-1 = pt pt-1. Note: rt= ln(1+rt) = (x-0)k/k! x dk/dxk(ln(1+x)) = x x2/2 + x3/3 + ~x. 3)ln(1+0. 5)=. 405 ~ 0. 05 (pt/pt-k) = (1+rt-i+1) ln (pt/pt-k) = ln(1+rt-i+1) Rt = pt + dt pt-1 / pt-1 = pt + dt / pt-1 1. A : if a1,a2,a3 a (countable set) then, the union of it exists in a also uai a. Eg: a = { , , 2 = power set of ie. the set of all subsets of , = {0,1,2,3}, a={ , ,{0,1,2},{3}} This is the -field generated by the following sets: the open intervals (in r) ie {(a,b) , a,b r a
