Exact solutions of some exit times for the diffusion risk model with liquid reserves, credit and debit interest

Abstract

The diffusion risk model is considered in the presence of liquid reserves, credit and debit interest. For arbitrary boundary and any interval, the Laplace-Stieltjes transform (LST) of some exit times of the risk process are derived. The results are then used to find the probability and mathematical expectation of the exit times. Finally, several numerical examples be discussed in order to illustrate the applications of the LST of some exit times.

Keywords:

• Exit times
• Strong Markov property
• Confluent hypergeometric functions
• Operators
• Martingale

Additional information

Funding

This work was supported by MOE (Ministry of Education in China) Youth Project of Humanities and Social Sciences (Project No.14YJCZH048,15YJCZH204), National Natural Science Foundation of China (Grant No.11401436, 11601382).