کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1157131 958940 2006 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On an approximation problem for stochastic integrals where random time nets do not help
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
On an approximation problem for stochastic integrals where random time nets do not help
چکیده انگلیسی

Given a geometric Brownian motion S=(St)t∈[0,T]S=(St)t∈[0,T] and a Borel measurable function g:(0,∞)→Rg:(0,∞)→R such that g(ST)∈L2g(ST)∈L2, we approximate g(ST)-Eg(ST)g(ST)-Eg(ST) by∑i=1nvi-1(Sτi-Sτi-1)where 0=τ0⩽⋯⩽τn=T0=τ0⩽⋯⩽τn=T is an increasing sequence of stopping times and the vi-1vi-1 are Fτi-1Fτi-1-measurable random variables such that Evi-12(Sτi-Sτi-1)2<∞ ((Ft)t∈[0,T](Ft)t∈[0,T] is the augmentation of the natural filtration of the underlying Brownian motion). In case that g   is not almost surely linear, we show that one gets a lower bound for the L2L2-approximation rate of 1/n if one optimizes over all nets consisting of n+1n+1 stopping times. This lower bound coincides with the upper bound for all reasonable functions g in case deterministic time-nets are used. Hence random time nets do not improve the rate of convergence in this case. The same result holds true for the Brownian motion instead of the geometric Brownian motion.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 116, Issue 3, March 2006, Pages 407–422
نویسندگان
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