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

IF 1 2区数学 Q3 STATISTICS & PROBABILITY

Probability Uncertainty and Quantitative Risk Pub Date : 2018-06-05 DOI:10.1186/s41546-018-0030-2

Ludger Overbeck, Jasmin A. L. Röder

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引用次数: 0

摘要

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。

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

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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来源期刊

Probability Uncertainty and Quantitative Risk STATISTICS & PROBABILITY-

CiteScore

1.60

自引率

13.30%

发文量

审稿时长

12 weeks

期刊介绍： Probability, Uncertainty and Quantitative Risk (PUQR) is a quarterly academic journal under the supervision of the Ministry of Education of the People's Republic of China and hosted by Shandong University, which is open to the public at home and abroad (ISSN 2095-9672; CN 37-1505/O1). Probability, Uncertainty and Quantitative Risk (PUQR) mainly reports on the major developments in modern probability theory, covering stochastic analysis and statistics, stochastic processes, dynamical analysis and control theory, and their applications in the fields of finance, economics, biology, and computer science. The journal is currently indexed in ESCI, Scopus, Mathematical Reviews, zbMATH Open and other databases.