Parisian types of ruin probabilities for a class of dependent risk-reserve processes
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Parisian types of ruin probabilities for a class of dependent risk-reserve processes. / Bladt, Mogens; Nielsen, Bo Friis; Peralta, Oscar.
In: Scandinavian Actuarial Journal, Vol. 2019, No. 1, 02.01.2019, p. 32-61.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Parisian types of ruin probabilities for a class of dependent risk-reserve processes
AU - Bladt, Mogens
AU - Nielsen, Bo Friis
AU - Peralta, Oscar
PY - 2019/1/2
Y1 - 2019/1/2
N2 - For a rather general class of risk-reserve processes, we provide an exact method for calculating different kinds of ruin probabilities, with particular emphasis on variations over Parisian type of ruin. The risk-reserve processes under consideration have, in general, dependent phase-type distributed claim sizes and inter-arrivals times, whereas the movement between claims can either be linear or follow a Brownian motion with linear drift. For such processes, we provide explicit formulae for classical, Parisian and cumulative Parisian types of ruin (for both finite and infinite time horizons) when the clocks are phase-type distributed. An erlangization scheme provides an efficient algorithmic methods for calculating the aforementioned ruin probabilities with deterministic clocks. Special attention is drawn to the construction of specific dependency structures, and we provide a number of numerical examples to study its effect on probabilities.
AB - For a rather general class of risk-reserve processes, we provide an exact method for calculating different kinds of ruin probabilities, with particular emphasis on variations over Parisian type of ruin. The risk-reserve processes under consideration have, in general, dependent phase-type distributed claim sizes and inter-arrivals times, whereas the movement between claims can either be linear or follow a Brownian motion with linear drift. For such processes, we provide explicit formulae for classical, Parisian and cumulative Parisian types of ruin (for both finite and infinite time horizons) when the clocks are phase-type distributed. An erlangization scheme provides an efficient algorithmic methods for calculating the aforementioned ruin probabilities with deterministic clocks. Special attention is drawn to the construction of specific dependency structures, and we provide a number of numerical examples to study its effect on probabilities.
KW - (cumulative) Parisian ruin
KW - Baker copula
KW - Brownian motion
KW - dependency
KW - erlangization
KW - fluid flow
KW - Lévy process
KW - order statistics
KW - phase-type distributions
KW - ruin probability
KW - Sparre-Andersen
UR - http://www.scopus.com/inward/record.url?scp=85049193535&partnerID=8YFLogxK
U2 - 10.1080/03461238.2018.1483420
DO - 10.1080/03461238.2018.1483420
M3 - Journal article
AN - SCOPUS:85049193535
VL - 2019
SP - 32
EP - 61
JO - Scandinavian Actuarial Journal
JF - Scandinavian Actuarial Journal
SN - 0346-1238
IS - 1
ER -
ID: 203596060