Geodesic
Exit problems for Kou's process in a Markovian environment
Teoriâ slučajnyh processov, Tome 25 (2020) no. 2, pp. 37-60

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we consider a path-wise sum of a Brownian motion plus a compound Poisson process with exponentially distributed positive and negative jumps with parameters that depend on some finite Markov chain. Using known fluctuation identities we investigate one-sided and two-sided exit problems generalizing some results for Kou's processes to the setting of regime switching models without exploiting the fluid embedding technique. The generating function for the hitting time of the state-dependent levels is analyzed. For the case of two states, the numerical examples are given.
Keywords: Kou process, regime-switching, state-dependent levels. 
@article{THSP_2020_25_2_a4,
     author = {Ie. Karnaukh},
     title = {Exit problems for {Kou's} process in a {Markovian} environment},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {37--60},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2020_25_2_a4/}
}
TY  - JOUR
AU  - Ie. Karnaukh
TI  - Exit problems for Kou's process in a Markovian environment
JO  - Teoriâ slučajnyh processov
PY  - 2020
SP  - 37
EP  - 60
VL  - 25
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2020_25_2_a4/
LA  - en
ID  - THSP_2020_25_2_a4
ER  - 
%0 Journal Article
%A Ie. Karnaukh
%T Exit problems for Kou's process in a Markovian environment
%J Teoriâ slučajnyh processov
%D 2020
%P 37-60
%V 25
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2020_25_2_a4/
%G en
%F THSP_2020_25_2_a4
Ie. Karnaukh. Exit problems for Kou's process in a Markovian environment. Teoriâ slučajnyh processov, Tome 25 (2020) no. 2, pp. 37-60. http://geodesic.mathdoc.fr/item/THSP_2020_25_2_a4/