Abstract and Applied Analysis

The Exit Time and the Dividend Value Function for One-Dimensional Diffusion Processes

Peng Li, Chuancun Yin, and Ming Zhou

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Abstract

We investigate the exit times from an interval for a general one-dimensional time-homogeneous diffusion process and their applications to the dividend problem in risk theory. Specifically, we first use Dynkin’s formula to derive the ordinary differential equations satisfied by the Laplace transform of the exit times. Then, as some examples, we solve the closed-form expression of the Laplace transform of the exit times for several popular diffusions, which are commonly used in modelling of finance and insurance market. Most interestingly, as the applications of the exit times, we create the connect between the dividend value function and the Laplace transform of the exit times. Both the barrier and threshold dividend value function are clearly expressed in terms of the Laplace transform of the exit times.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 675202, 9 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393512145

Digital Object Identifier
doi:10.1155/2013/675202

Mathematical Reviews number (MathSciNet)
MR3132523

Zentralblatt MATH identifier
07095222

Citation

Li, Peng; Yin, Chuancun; Zhou, Ming. The Exit Time and the Dividend Value Function for One-Dimensional Diffusion Processes. Abstr. Appl. Anal. 2013 (2013), Article ID 675202, 9 pages. doi:10.1155/2013/675202. https://projecteuclid.org/euclid.aaa/1393512145


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