CBI-time-changed Levy processes

被引：0

作者：

Fontana, Claudio ^{[1
]}

Gnoatto, Alessandro ^{[2
]}

Szulda, Guillaume ^{[3
]}

机构：

[1] Univ Padua, Dept Math Tullio Levi Civita, Padua, Italy

[2] Univ Verona, Dept Econ, Verona, Italy

[3] Ecole Ponts, CERMICS, Marne La Vallee, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2023年 / 163卷

关键词：

Branching process; Change of time; Affine process; Stochastic volatility; Moment explosion; STOCHASTIC VOLATILITY; BRANCHING-PROCESSES; AFFINE PROCESSES; VARIANCE; MODEL;

D O I：

10.1016/j.spa.2023.06.005

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We introduce and study the class of CBI-time-changed Levy processes (CBITCL), obtained by time-changing a Levy process with respect to an integrated continuous-state branching process with immigration (CBI). We characterize CBITCL processes as solutions to a certain stochastic integral equation and relate them to affine stochastic volatility processes. We provide a complete analysis of the time of explosion of exponential moments of CBITCL processes and study their asymptotic behavior. In addition, we show that CBITCL processes are stable with respect to a suitable class of equivalent changes of measure. As illustrated by some examples, CBITCL processes are flexible and tractable processes with a significant potential for applications in finance.& COPY; 2023 Elsevier B.V. All rights reserved.

引用

页码：323 / 349

页数：27

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