TY - JOUR
T1 - Potential measures for spectrally negative Markov additive processes with applications in ruin theory
AU - Feng, Runhuan
AU - Shimizu, Yasutaka
N1 - Funding Information:
We would like to thank Dr. Jevgenijs Ivanovs for bringing to our attention his recent work Ivanovs (2013) on the subject. The invaluable suggestions from Dr. Ivanovs and the anonymous referee for improving the paper are greatly appreciated. This research has been partially supported by the Ministry of Education, Science, Sports and Culture , Grant-in-Aid for Young Scientists (B), no. 24740061 , 2013–2014, and Japan Science and Technology Agency, CREST .
Publisher Copyright:
© 2014 Elsevier B.V.
PY - 2014/12/1
Y1 - 2014/12/1
N2 - The Markov additive process (MAP) has become an increasingly popular modeling tool in the applied probability literature. In many applications, quantities of interest are represented as functionals of MAPs and potential measures, also known as resolvent measures, have played a key role in the representations of explicit solutions to these functionals. In this paper, closed-form solutions to potential measures for spectrally negative MAPs are found using a novel approach based on algebraic operations of matrix operators. This approach also provides a connection between results from fluctuation theoretic techniques and those from classical differential equation techniques. In the end, the paper presents a number of applications to ruin-related quantities as well as verification of known results concerning exit problems.
AB - The Markov additive process (MAP) has become an increasingly popular modeling tool in the applied probability literature. In many applications, quantities of interest are represented as functionals of MAPs and potential measures, also known as resolvent measures, have played a key role in the representations of explicit solutions to these functionals. In this paper, closed-form solutions to potential measures for spectrally negative MAPs are found using a novel approach based on algebraic operations of matrix operators. This approach also provides a connection between results from fluctuation theoretic techniques and those from classical differential equation techniques. In the end, the paper presents a number of applications to ruin-related quantities as well as verification of known results concerning exit problems.
KW - Exit problems
KW - Markov additive processes
KW - Markov renewal equation
KW - Potential measure
KW - Resolvent density
KW - Scale matrix
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U2 - 10.1016/j.insmatheco.2014.08.001
DO - 10.1016/j.insmatheco.2014.08.001
M3 - Article
AN - SCOPUS:84907814737
SN - 0167-6687
VL - 59
SP - 11
EP - 26
JO - Insurance: Mathematics and Economics
JF - Insurance: Mathematics and Economics
ER -