Frontiers of Mathematics in China >

2016 , Vol. 11 >Issue 3: 737 - 751

DOI: https://doi.org/10.1007/s11464-016-0521-3

RESEARCH ARTICLE

Ornstein-Uhlenback type Omega model

  • Xiulian WANG 1 ,
  • Wei WANG , 1 ,
  • Chunsheng ZHANG 2
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  • 1. College of Mathematical Science, Tianjin Normal University, Tianjin 300387, China
  • 2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China

Received date: 22 Oct 2014

Accepted date: 05 Jan 2016

Published date: 17 May 2016

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

We consider the Omega model with underlying Ornstein-Uhlenbeck type surplus process for an insurance company and obtain some useful results. Explicit expressions for the expected discounted penalty function at bankruptcy with a constant bankruptcy rate and linear bankruptcy rate are derived. Based on random observations of the surplus process, we examine the differentiability for the expected discounted penalty function at bankruptcy especially at zero. Finally, we give the Laplace transforms for occupation times as an important example of Li and Zhou [Adv. Appl. Probab., 2013, 45(4): 1049–1067].

Key words： Omega model; Ornstein-Uhlenbeck type Omega model; probability of bankruptcy; Gerber-Shiu function at bankruptcy; occupation time

Cite this article

Xiulian WANG , Wei WANG , Chunsheng ZHANG . Ornstein-Uhlenback type Omega model[J]. Frontiers of Mathematics in China, 2016 , 11(3) : 737 -751 . DOI: 10.1007/s11464-016-0521-3

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