Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1199.91075
Dong, Hailing; Hou, Zhenting; Zhang, Xina
The probability of ruin in a kind of Markov-modulated risk model. (English)
[J] Chin. J. Eng. Math. 26, No. 3, 381-388 (2009). ISSN 1005-3085

Summary: In this paper, the probability of ruin is investigated in a Markov-modulated risk model, in which the claim inter-arrives and claim sizes are influenced by an external Markovian process, and the premium rate depends on the external Markovian process and the level of company's reserves. We consider not only that stochastic environment influences the insurance company, but also that the insurance company adjusts premium according to the level of reserves to attract new customers. So the risk model is closer to reality and more accessible to be applied. By using the backward differential argument and the Markov property of the external process, we derive the integral equation satisfied by the probability of ruin. Further, we solve the equation by Laplace transforms. Finally, an example is given to illustrate the feasibility and effectiveness of the obtained theoretical results.

MSC 2000:: *91B30 Risk theory etc.
60K37 Processes in random environments

Keywords: ruin probability; Markov-modulated; interest rate; Laplace-transforms

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]