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DTSTART:20181104T020000
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DTSTART:20190310T020000
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UID:calendar.1329.field_event_date.0@uwaterloo.ca/statistics-and-actuarial-
science
DTSTAMP:20190822T152813Z
CREATED:20190122T132343Z
DESCRIPTION:Risk Aggregation: A General Approach via the Class of Generaliz
ed Gamma Convolutions\n\n\n\nRisk aggregation is virtually everywhere in i
nsurance applications. Indeed\, in the vast majority of situations insurer
s are interested in the properties of the sums of the risks they are expos
ed to\, rather than in the stand-alone risks per se. Unfortunately\, the p
roblem of formulating the probability distributions of the aforementioned
sums is rather involved\, and as a rule does not have an explicit solution
. As a result\, numerous methods to approximate the distributions of the s
ums have been proposed\, with the moment matching approximations (MMAs) be
ing arguably the most popular. The arsenal of the existing MMAs is quite i
mpressive and contains such very simple methods as the normal and shifted-
gamma approximations that\, respectively\, match the first two and three m
oments\, only\, as well as such much more intricate methods as the one bas
ed on the mixed Erlang distributions. Note however that in practice the su
ms of insurance risks can have numerous and just a few summands\; in the l
atter case the normal\n\n\n\napproximation is very questionable. Also\, in
practice the distributions of the stand-alone risks can be light-tailed o
r heavy-tailed\; in the latter case moments of higher orders (e.g.\, secon
d\, etc.) may not exist\, and so the approximation based on mixed Erlang d
istributions is of limited usefulness. In this talk I will reveal a refine
d MMA method for approximating the distributions of the sums of insurance
risks. The method approximates the distributions of interest to any desire
d precision\, works equally well for light and heavy-tailed distributions\
, and is reasonably fast irrespective of the number of the involved summan
ds. (This is a joint work with Justin Miles and Alexey Kuznetsov\, York Un
iversity.)
DTSTART;TZID=America/Toronto:20190308T103000
DTEND;TZID=America/Toronto:20190308T103000
LAST-MODIFIED:20190227T161906Z
LOCATION:M3 - Mathematics 3\n \n\n Room: 3127 \n
\n\n \n\n 200 University Avenue West \n
Waterloo\, ON\n
N2L 3G1\n \nCanada
SUMMARY:Department seminar by Ed Furman\, York University
URL;TYPE=URI:https://uwaterloo.ca/statistics-and-actuarial-science/events/d
epartment-seminar-ed-furman-york-university
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