On an approximation problem for stochastic integrals where random time nets do not help

Abstract

Given a geometric Brownian motion S=(St)t∈[0,T] and a Borel measurable function g:(0,∞)→R such that g(ST)∈L2, we approximate g(ST)-Eg(ST) by∑i=1nvi-1(Sτi-Sτi-1)where 0= τ0≤⋯≤τn=T is an increasing sequence of stopping times and the vi-1 are Fτi-1-measurable random variables such that Evi-12(Sτi-Sτi-1)2