Loss Minimization Technique - Risk Management and Insurance, Principles of Insurance Video Lecture | Principles of Insurance - B Com

all right welcome to Manson Ellie's math
lab this was a requested topic I
proposed it and enough people liked it
that I think it's worth going over I
want to go over a specific reserving
technique called the chain ladder method
so this is the most basic method I would
say and it is one of the techniques used
for predicting or projecting ultimate
losses so what's the idea basic idea
behind reserving is that say you're an
insurance company you need to set aside
some money or some assets assets that
will cover your future liabilities
because you want to remain solvent okay
if you were over reserving that can be a
problem because you're setting aside
money that could be used to cover
expenses it could be used for investing
so that's an issue if you're under
reserving then you don't have enough
money to pay off your debts so that's
definitely a problem as well so either
way it's an issue so we want to get our
reserve estimates right if possible but
their estimates so how can we estimate
estimate the ultimate losses using this
technique so one this is called a
developmental triangle this is called a
reported loss triangle I should say in
this case and what a reported losses so
reported losses are just the paid losses
plus case losses so a claims adjuster
may claim may have come in and the
claims adjuster decides we need to set
aside some money now some of this money
will be paid immediately to the insured
and some of this money and that's the
paid losses some of this money will be
set aside in order to eventually be paid
to them that's the case losses okay and
these things are updated right so that's
what reported losses are and so in our
case here
and I'm assuming that we're in calendar
year 2010 quarter one so that's why I
have that right here we're assuming that
we're in the time 2010 quarter one and
that's what I have right here three
months out of 2010's 2010 quarter one
right so um excuse me
some water
alright and so if we look back we have
our data our historical data if we look
back at say accident near 2000 2000
first of all what does it represent
these are this row row four
these are the actual reported losses
corresponding to accidents that occurred
in 2000 so according to our historical
data 328 reported losses happened within
the first three months then also
corresponding to accident new 2000 we
have 778 reported losses 15 months out
and these are cumulative so actually
what's the change the difference here is
how much of these reported losses
actually happened at 15 months out and
we keep going so once we get a 27 months
out at fracks in New Yor 2000 we have
eleven hundred and seventy eight
reported losses etc now notice that once
we get out to a hundred and eleven
months out out here we see that
hopefully these reported losses are
fully developed and we're hoping that
we're not gonna have to report any more
now that could change depending on
different things but I'm gonna go into
that okay so we have those accent years
I just we just do this we have this for
each of these right and hopefully you
see actually that we're what calendar
year is this number end to five seven
eight this is a hundred and twenty three
months out
four oxen year 2000 this puts us in the
current calendar year in quarter so this
is basically represents the reported
losses for oxen or 2010 today right
because we're in I'm assuming we're in
calendar year 2010 quarter one this
diagonal actually represents calendar
year 2010 quarter one so hopefully that
makes sense okay and now the underlying
assumption of this method is that losses
will develop according to how they've
developed in the past so we're using
historical trends historical lost
development patterns to predict who
projects how will losses today it today
or more recently develop and what we the
way that we quantify that is by with
using these development factors so here
are my linked ratios and these are also
just development factors and what these
represent 2.37 this is just the quotient
of 778 divided by 328 so this again this
number right here represents the
quotient of 778 and 328 so we're saying
here is basically this gives us an
estimate of how reported losses three
months out from an accident year develop
to the next year so according to
historical data for taxing year 2000
multiplying 328 times two point three
seven gives me 778 this gives us an idea
of how those losses are developing and
similarly we can just go down this so
all this is nothing confusing really
these are all just the quotient so this
is two point three two is just seven
ninety divided by three forty two point
two four is just eight fourteen divided
by three sixty four one point three is
just 15 28 divided by eleven seventy
eight
so we're getting each of these numbers
is representing basically for instance
right here 1.3 it's saying how have
reported losses developed from 27 months
to 39 months four acts in year 2010 all
right so hopefully that makes sense
so this is our developmental triangle
here our loss developmental triangle and
from this we get averages and the reason
we're doing these averages because we
want to again say we're looking at three
months of development which is
corresponding to the current calendar
year and also acts in here in 2010
quarter one we want to say how much has
this 363 developed well this is in
developmental period three months all of
these cells in column one from eight row
18 to row 27 these all represent
historical trends for which these
represent how losses have developed from
3 to 15 months so each of these
potentially could be used to help us
indicate how have how will this 363
develop if I put it in here like in
other words what will this number be
how will the reported losses have
developed I mean we basically have a
choice mean which one of these would we
use that's what we take averages and I
think it makes sense to give the more
recent data a heavier weight because
hopefully that's more accurate that's
more maybe more accurate about how
things have been going so what we'll do
here is we'll take different types of
averages we may have a 3-year volume I
may have a 5-year volume may have it's
for your simple with 5 year simple known
as the geometric mean is also given the
square root of the product so these are
my fits just two averages and I'm here
if my preference is here I'm just
selecting actually the three-year simple
now don't be throwing off here it looks
like these are exactly the same
it looks like the three-year volume and
the three are simple or exactly the same
whether or not if I change how things
are rounded if I change how things are
rounded here and then you'll see these
are actually different
so notices the numbers are actually
different right the farther I go out the
more of those change so those averages
are not the same but for our purposes
just trying to keep things simple I'm
taking my selected average these are the
ones I'm going to use I'm gonna use row
33 and how do we get the selected
actuarial judgment experience so we're
taking row 33 and these are going to be
the ones I'm going to use actually these
are the developmental factors I'm going
to use to project my reported losses
forward so in other words what is this
2.31 represent this represents if I
multiply 363 this is the reported loss
in calendar year 2010 Quarter 1
corresponding to acts in year 2000 if I
multiply 363 times two point three one
that will give me what I have an
estimate for the reported loss
cumulative for 15 months out of 2010
right and if I took one point five one
and multiplied by 791 right this is the
de la Spellman factor saying how do we
get from 15 months out to 27 months out
well these things develop by a factor of
1.5 one so if I take one point 5 1
multiplied by 791 that will give me this
entry here this estimate of what these
reported losses in acts and year 2009
what they will be when they've developed
27 months out so hopefully you're
getting the flavor there and we just
keep going so now because uh again
because for instance for 2010 Quarter 1
I'm not just interested in how they
developed to the next period I want to
know what is the value gonna be once
it's fully developed once its way out
here I want to know what the reported
loss is going to be once they basically
been exhausted once there there are no
more losses that were being reported so
what I want to do is I want to multiply
363 times two point three one then two
then take that multiplied by 1 point 5
take that x 1.29 again I'm getting these
numbers right here these this is telling
me how these losses are developing so
I'm looking right here and I'm just
multiplying those that's why I have what
are called as CD f's CD f's which again
they're not the cumulative distribution
functions these are the cumulative
developmental factors 7.38 is the
product of two point three one with one
point five one go all the way down this
row what does that represent think about
what I just said seven point three eight
should give me an estimate of the
reported loss in accident year 2010 it
will give me an estimate of what this
reported loss will be once it is fully
developed the seven point three eight is
the factor the developmental factor
which will give me an estimate of the
reported losses for accident near 2010 I
want to know what they're gonna be at
the end right once they are fully
developed so that's what that will give
me so I hope that makes sense and that
again I mean the logic there is just is
corresponding to these selected LDS
right
if I multiply 363 times two point three
one it gives me the ultimate here or it
gives me the reported loss here
multiplied by one point five one that
will give me the ultimate here etc and
seven point three eight is the product
of all these so what's doing the exact
same thing so again well just illustrate
further what would I use three point two
CDF for that would give me the projected
fully developed loss corresponding to
acts in here 2009 so in other words if I
multiply three point two times 791 that
will give me an estimate for how much
this reported loss will be once it's
fully developed once its way out here
once it's everything's happened right so
I hope that makes sense so that's the
idea and now I'll just do what I just
said
so I'm gonna take my my recent reported
losses
just think about this intuitively what
should recent reported losses be this is
just saying well what you're in quarter
are we in what I said to this example is
that we're in calendar year 2010 quarter
one right what are the recent reported
losses is just a diagonal it's just this
diagonal these diagonal entries are the
recent reported losses again we want to
get an estimate for what these reported
losses will be once they're fully
developed this one has already fully
developed possibly according to their
historical data this looks like it's
floyd evelopment looks like it might be
according to the previous year accent
area it looks like it's May fully
developed but ok but maybe it needs to
be told more of this one paw needs to be
developed more etc right so I take my
recent my recent reported losses that's
just the diagonal of my reported loss
triangle okay and then I multiply them
by the CDF as I mentioned so as I
mentioned before taking three zero point
seven eight times three point six three
gives me an estimate for my projected
ultimate loss so again to reiterate what
does this cell represent this represents
basically how much we need to reserve
how much we need to store away that will
cover the reported losses from accident
year 2010 based off our historical
trends we think using this specific
reserving method that for the losses and
acts in year 2010 that they will develop
when they're developed fully that will
get this numerical value of 2684
accident near 2009 remember that this
791 this had already developed one
period right right here I want to know
what will be its projectile to loss when
I go all the way out in order to do that
I use this particular CDF so that's what
I've done so this number 25 through 32
is the prod
of 791 and 3.2 so take these multiply
them together this gives me an estimate
this estimate represents how much we
need to set aside to cover our reported
losses for acts in year 2009 etc notice
go all the way down here go all the way
down to 2000 the year 2000 and these
losses as we saw according to what we
have the data says is that these are
fully developed we have a 2 5 7 8 and
there's nowhere else for it to go that's
it 2 5 7 8 alright the last thing I
wanted to basically share so that that
gives us away I guess a way to get the
reject gentlemen losses and actually
have one more row what's the IBNR and
Kurd but not reported these are just
basically what are incurring losses
these are just basically the amount
incurred loss for the insurance company
in this case is just um what amount they
have to pay out those are the incurred
losses so for accident 2010 we had
incurred losses of 363 but our projected
ultimate loss for accident 2010 is two
thousand six hundred and eighty so what
are the losses that are incurred but not
reported which is the difference we
think that this number will be incurred
total and these this number have been
reported so incurred not reported but
not reported is just twenty two thousand
six hundred eighty minus 363 does my
encouraged been reported these numbers
are important right because these are
basically represent what are the
reported losses that were eventually
gonna have to pay out and so as you can
see for two thousand hopefully weren't
gonna pay out anything else because
everything for the year two thousand
it's far enough back that hopefully it's
fully developed alright so last thing I
wanted to share is just and this is
important this last bit because they we
want to know how stable is this method
so in other words right now we're
evaluating where
determining these projected losses as of
the year the calendar year 2010 quarter
1 what would they have been if I had
predicted them if I had estimated these
ultimate losses say in calendar year
2009 and actually I can change this I
can change this to reflect that and
that's what I've done here and this is
again this isn't um these numbers are
not of course accurate really I mean
they just made these up I mean I gave a
little bit of thought to them but what
if I changed this to 2009 quarter one
notice my numbers change this projected
ultimate loss change actually we do that
one more time so let me go back to 2010
quarter one the ultimate loss was two
thousand six hundred eighty so this is
our estimate for evaluation period for
today four dozen 1 2010 quarter one what
if I think about a like what would the
estimate have been had we the present
time band 2009 quarter one it drops to
two two thousand two thousand dollars
four hundred twenty seven so if we're in
a calendar year 2009 quarter one and we
run our estimates notice that these are
all a little bit lower so based off
historical trends we get a lower
projected ultimate loss than before and
then we imagine we are year passes and
now we're back in president Day 2010 the
quarter one and now our project ultimate
losses are two six eight zero think of
our second that can be an issue because
basically what that saying is that for
accident in 2010 we did not set aside
enough money and so that's what I have
down here so I have my charts okay so I
have three of them um I have 2007 2008
2009 so what is this saying this is
saying that if we're in calendar year
2007 quarter one and I project
my ultimate losses for that accident
year what would they have been they
would have been about 20 150 or so this
represents what I would have projected
as my ultimate losses had I been in
calendar year 2007 a year passes I do
the estimate again I use a chain ladder
method I run the whole analysis again I
get my projected ultimate losses for
that same accident near 2007 and I say
what am i Altima losses now well damn it
they're 2300 that means if I'm the
insurance company to set aside more
money that's not really good I mean
because we weren't right of course is
your estimates but I need to set aside
more money the next year another year
goes by is now a 2009 quarter 1 this is
say I need to set aside even more money
I'm setting aside more money as time
goes by I'm basically I'm saying as time
goes by my estimate was too low I needed
actually to set aside more money to
cover the reported losses for axon year
2007 finally to the current year and I
say damn it I was way off I actually
need to set aside almost $2,600 to cover
my 2007 accident near losses and I look
along 2008 same idea same idea of 2009
so that's not what we want right
and of course management everything's
fine I'm not gonna be too happy about
that because they want you I mean what
would be the ideal situation the ideal
situation hopefully you would you'd say
to yourself is that that these bars
would just be level I mean let's say
that the actual ultimate losses are 2600
then what we would hope is that our
projected ultimate losses each
evaluation period each calendar year in
quarter would be around 2600 then we
would say well that's great I mean we we
estimated these losses quite accurately
and furthermore if they were level bars
like this we wouldn't have to keep
setting aside money more and more money
to cover what we think these reported
losses will be
all right so um that pretty much does it
again this is very basic overview of the
chain ladder preserving method there are
several different types of reserving
methods and hopefully you can see why
because if I just ran the analysis for
this method we're not getting very good
estimates what we would say actually
here is that this chain ladder method is
unstable we want things to be stable I
want this to be flat so we may want to
resort to other reserving techniques
that will hopefully give us a more
stable projected ultimate loss so hope
you found this helpful I think this was
a good idea because I'm for people
entering the profession you really have
no idea what goes on so this is one of
the more traditional roles that an
actuary has is reserving so please give
the video a thumbs up and tell me what
you think and thanks for watching