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A Time-Homogeneous Diffusion Model with Tax

Part of: Applications Markov processes Special processes Mathematical economics Stochastic processes

Published online by Cambridge University Press:  30 January 2018

Bin Li ,
Qihe Tang  and
Xiaowen Zhou
Bin Li*
Affiliation:
University of Iowa
Qihe Tang*
Affiliation:
University of Iowa
Xiaowen Zhou*
Affiliation:
Concordia University
*
∗ Postal address: Applied Mathematical and Computational Sciences Program, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242, USA. Email address: [email protected]
∗∗ Postal address: Department of Statistics and Actuarial Science, University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA. Email address: [email protected]
∗∗∗ Postal address: Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec, H3G 1M8, Canada. Email address: [email protected]
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Abstract

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We study the two-sided exit problem of a time-homogeneous diffusion process with tax payments of loss-carry-forward type and obtain explicit formulae for the Laplace transforms associated with the two-sided exit problem. The expected present value of tax payments until default, the two-sided exit probabilities, and, hence, the nondefault probability with the default threshold equal to the lower bound are solved as immediate corollaries. A sufficient and necessary condition for the tax identity in ruin theory is discovered.

Keywords

Diffusionhitting timeLaplace transformMarkov propertytaxtwo-sided exit problem

MSC classification

Primary: 62P05: Applications to actuarial sciences and financial mathematics
Secondary: 60J60: Diffusion processes 60G40: Stopping times; optimal stopping problems; gambling theory 60K15: Markov renewal processes, semi-Markov processes 91B30: Risk theory, insurance
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 1 , March 2013 , pp. 195 - 207
Copyright
Copyright © Applied Probability Trust 2013 

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