The stochastic Leibniz formula for Volterra integrals under enlarged filtrations

IF 0.5 4区 数学 Q4 STATISTICS & PROBABILITY
Markus Hess
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引用次数: 1

Abstract

In this paper, we derive stochastic Leibniz formulas for Volterra integrals under enlarged filtrations. We investigate both pure-jump and Brownian Volterra processes under diverse initially enlarged filtration approaches. In these setups, we compare the ordinary with the stochastic (Doléans-Dade) exponential of a Volterra process and provide the corresponding martingale conditions. We also consider backward stochastic Volterra integral equations (BSVIEs) under enlarged filtrations and obtain the related solution formulas. We finally propose an anticipative Heath Jarrow Morton (HJM) forward rate model of Volterra-type and infer the associated bond price representation. In an introductory section, we compile various facts on deterministic and stochastic Leibniz formulas for parameter integrals.
放大过滤条件下Volterra积分的随机莱布尼兹公式
本文导出了放大过滤条件下Volterra积分的随机莱布尼兹公式。我们在不同的初始放大过滤方法下研究了纯跳跃和布朗沃尔泰拉过程。在这些设置中,我们比较了Volterra过程的普通指数和随机指数(dolans - dade),并提供了相应的鞅条件。我们还考虑了放大过滤条件下的倒向随机Volterra积分方程(BSVIEs),并得到了相关的求解公式。最后,我们提出了一个具有volterra型的预期Heath Jarrow Morton (HJM)远期利率模型,并推导了相关债券价格的表示。在介绍部分,我们汇编了关于参数积分的确定性和随机莱布尼茨公式的各种事实。
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来源期刊
Stochastic Models
Stochastic Models 数学-统计学与概率论
CiteScore
1.30
自引率
14.30%
发文量
42
审稿时长
>12 weeks
期刊介绍: Stochastic Models publishes papers discussing the theory and applications of probability as they arise in the modeling of phenomena in the natural sciences, social sciences and technology. It presents novel contributions to mathematical theory, using structural, analytical, algorithmic or experimental approaches. In an interdisciplinary context, it discusses practical applications of stochastic models to diverse areas such as biology, computer science, telecommunications modeling, inventories and dams, reliability, storage, queueing theory, mathematical finance and operations research.
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