کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1155981 958790 2011 22 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Random times with given survival probability and their FF-martingale decomposition formula
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Random times with given survival probability and their FF-martingale decomposition formula
چکیده انگلیسی

Given a filtered probability space (Ω,F=(Ft)t≥0,P)(Ω,F=(Ft)t≥0,P), an FF-adapted continuous increasing process ΛΛ and a positive (P,F)(P,F) local martingale NN such that Zt:=Nte−Λt satisfies Zt≤1,t≥0Zt≤1,t≥0, we construct probability measures QQ and a random time ττ on an extension of (Ω,F,P)(Ω,F,P), such that the survival probability of ττ, i.e., Q[τ>t|Ft]Q[τ>t|Ft] is equal to ZtZt for t≥0t≥0. We show that there exist several solutions and that an increasing family of martingales, combined with a stochastic differential equation, constitutes a natural way to construct these solutions. Our extended space will be equipped with the enlarged filtration G=(Gt)t≥0G=(Gt)t≥0 where GtGt is the σσ-field ∩s>t(Fs∨σ(τ∧s))∩s>t(Fs∨σ(τ∧s)) completed with the QQ-negligible sets. We show that all (P,F)(P,F) martingales remain GG-semimartingales and we give an explicit semimartingale decomposition formula. Finally, we show how this decomposition formula is intimately linked with the stochastic differential equation introduced before.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 121, Issue 6, June 2011, Pages 1389–1410
نویسندگان
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