Stochastic areas of diffusions and applications

Zhenyu Cui; Jingtang Ma

doi:10.1016/j.jmaa.2015.11.055

Stochastic areas of diffusions and applications

Zhenyu Cui
, Jingtang Ma

School of Business

Southwestern University of Finance and Economics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this paper we study the stochastic area swept by a regular time-homogeneous diffusion till a stopping time. This unifies some recent literature in this area. Through stochastic time-change we establish a link between the stochastic area and the stopping time of another associated time-homogeneous diffusion. Then we characterize the Laplace transform and integer moments of the stochastic area in terms of the eigenfunctions of the associated diffusion. We show applications of the results to a new structural model of default (Yildirim [28]) and the Omega risk model of bankruptcy in risk analysis (Gerber, Shiu and Yang [11]).

Original language	English
Pages (from-to)	79-93
Number of pages	15
Journal	Journal of Mathematical Analysis and Applications
Volume	436
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2015.11.055
State	Published - 1 Apr 2016

Keywords

Azema-Yor stopping time
Dambis-Dubins-Schwartz Brownian motion
Omega risk model
Risk model with tax
Time-change
Time-homogeneous diffusion

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10.1016/j.jmaa.2015.11.055

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title = "Stochastic areas of diffusions and applications",

abstract = "In this paper we study the stochastic area swept by a regular time-homogeneous diffusion till a stopping time. This unifies some recent literature in this area. Through stochastic time-change we establish a link between the stochastic area and the stopping time of another associated time-homogeneous diffusion. Then we characterize the Laplace transform and integer moments of the stochastic area in terms of the eigenfunctions of the associated diffusion. We show applications of the results to a new structural model of default (Yildirim [28]) and the Omega risk model of bankruptcy in risk analysis (Gerber, Shiu and Yang [11]).",

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AU - Cui, Zhenyu

AU - Ma, Jingtang

PY - 2016/4/1

Y1 - 2016/4/1

N2 - In this paper we study the stochastic area swept by a regular time-homogeneous diffusion till a stopping time. This unifies some recent literature in this area. Through stochastic time-change we establish a link between the stochastic area and the stopping time of another associated time-homogeneous diffusion. Then we characterize the Laplace transform and integer moments of the stochastic area in terms of the eigenfunctions of the associated diffusion. We show applications of the results to a new structural model of default (Yildirim [28]) and the Omega risk model of bankruptcy in risk analysis (Gerber, Shiu and Yang [11]).

AB - In this paper we study the stochastic area swept by a regular time-homogeneous diffusion till a stopping time. This unifies some recent literature in this area. Through stochastic time-change we establish a link between the stochastic area and the stopping time of another associated time-homogeneous diffusion. Then we characterize the Laplace transform and integer moments of the stochastic area in terms of the eigenfunctions of the associated diffusion. We show applications of the results to a new structural model of default (Yildirim [28]) and the Omega risk model of bankruptcy in risk analysis (Gerber, Shiu and Yang [11]).

KW - Azema-Yor stopping time

KW - Dambis-Dubins-Schwartz Brownian motion

KW - Omega risk model

KW - Risk model with tax

KW - Time-change

KW - Time-homogeneous diffusion

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DO - 10.1016/j.jmaa.2015.11.055

M3 - Article

AN - SCOPUS:84953360317

SN - 0022-247X

VL - 436

SP - 79

EP - 93

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Stochastic areas of diffusions and applications

Abstract

Keywords

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