A Markov regenerative process with recurrence time and its application

Financial Innovation

Puneet Pasricha¹  Dharmaraja Selvamuthu¹ 

[1] Department of Mathematics, Indian Institute of Technology Delhi, 110016, New Delhi, India;

关键词: Non-homogeneous Markov regenerative process;    Recurrence times;    Markov renewal equation;    Credit ratings;    Default distribution;   

DOI  :  10.1186/s40854-021-00255-z

来源: Springer

【 摘 要 】

This study proposes a non-homogeneous continuous-time Markov regenerative process with recurrence times, in particular, forward and backward recurrence processes. We obtain the transient solution of the process in the form of a generalized Markov renewal equation. A distinguishing feature is that Markov and semi-Markov processes result as special cases of the proposed model. To model the credit rating dynamics to demonstrate its applicability, we apply the proposed stochastic process to Standard and Poor’s rating agency’s data. Further, statistical tests confirm that the proposed model captures the rating dynamics better than the existing models, and the inclusion of recurrence times significantly impacts the transition probabilities.

【 授权许可】

CC BY