Path-dependent backward stochastic Volterra integral equations with jumps, differentiability and duality principle

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2018-06-05 DOI:10.1186/s41546-018-0030-2

Ludger Overbeck, Jasmin A. L. Röder

引用次数: 0

Abstract

We study the existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations (BSVIEs) with jumps, where path-dependence means the dependence of the free term and generator of a path of a càdlàg process. Furthermore, we prove path-differentiability of such a solution and establish the duality principle between a linear path-dependent forward stochastic Volterra integral equation (FSVIE) with jumps and a linear path-dependent BSVIE with jumps. As a result of the duality principle we get a comparison theorem and derive a class of dynamic coherent risk measures based on path-dependent BSVIEs with jumps.

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具有跳跃、可微性和对偶原理的路径相关倒向随机Volterra积分方程

研究了具有跳变的路径相关倒向随机Volterra积分方程(BSVIEs)解的存在唯一性，其中路径相关是指càdlàg过程的路径自由项与生成项的相关性。进一步证明了该解的路径可微性，并建立了具有跳跃的线性路径相关正随机Volterra积分方程(FSVIE)与具有跳跃的线性路径相关BSVIE之间的对偶原理。利用对偶原理，得到了一个比较定理，并导出了一类基于具有跳跃的路径相关bsvie的动态相干风险测度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.