TY - JOUR
T1 - Stochastic areas of diffusions and applications
AU - Cui, Zhenyu
AU - Ma, Jingtang
N1 - Publisher Copyright:
© 2015 Elsevier Inc.
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
UR - http://www.scopus.com/inward/record.url?scp=84953360317&partnerID=8YFLogxK
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U2 - 10.1016/j.jmaa.2015.11.055
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 -