Popular in Sciences

Formal Sciences

Diameter rigidity for Kähler manifolds with positive bisectional curvature

Indian Institute of Science Ved Datar

Biology

Plasticity and microevolution of diatoms

University of Technology Sydney Martina Doblin

Chemistry

Statistical Mechanics for Chemistry and Materials Science

Indian Institute of Science Biman Bagchi

Chemistry

Polyfluorene-Wrapped Carbon Nanotubes Decorated with Photocleavable Side-Chains

McMaster University Alex Adronov

Biology

Analysis of rare coding variants reveals novel genetic risk factors for type 2 diabetes

University College London David Curtis

Life Sciences

The Mouse Cortical Connectome Maintains Specificity by Distinct Connectivity Profiles

Monash University Răzvan Gămănuţ

Formal Sciences

The Hybrid High-Order Method for Polytopal Meshes

Monash University

Rank-Based Multivariate Sarmanov for Modeling Dependence

View more insights in Sciences - Mathematics - Formal Sciences

View more figures from McMaster University

View the page of Anas Abdallah

Read the Study

Next in Formal Sciences

Software Testing of Generative AI Systems: Challenges and Opportunities

Aldeida Aleti | Monash University

Probabilistic Forecasting of Wind and Solar Farm Output

John Boland | University of South Australia

Anas Abdallah discusses the rank-based methods using the Sarmanov distribution to adequately estimate the loss reserves and properly capture the dependence between lines of business.

Image courtesy of interviewee. January 22, 2024

Log-in or Sign-up to Faculti
Currently viewing this subject insight as a guest. You have insight(s) remaining for this month. Login to view 8000+ figures on the platform.

Generating Workspace...

Export as PDF

This video video discusses the context of loss reserves for non-life insurance companies, differentiating them from life insurance companies. Non-life insurance covers areas such as auto and home insurance, requiring companies to set aside funds for future claims and to handle claims that have occurred but not yet been reported. The importance of managing reserves effectively, particularly considering the independence and interdependence of risks (e.g., due to natural disasters or pandemics), is emphasized.

Two main methodologies are presented for estimating dependence between risks in loss reserving: a multivariate approach using non-parametric models and a parametric approach based on copulas, which capture dependencies between risks. The rank-based method for estimating dependence is highlighted as a more robust option compared to conventional simultaneous estimation methods.

The proposed methodology combines rank-based estimation with flexible distributions, showing that this approach captures risk interdependencies better, thereby leading to a reduction in required risk capital and enhanced diversification benefits for insurance companies. The results from applying this methodology to real datasets from U.S. and Canadian insurance companies demonstrate its effectiveness.

This video video concludes by noting the relevance of this model in light of international regulations (IFRS 17), emphasizing its potential for improving solvency risk assessments and contributing positively to the economy and society as a whole.

Language:

Export as PDF

X-TIMESTAMP-MAP:LOCAL=00:00:00.000,MPEGTS=900000

00:00.065 --> 00:02.565
So this is the context and the, loss reserve

00:03.065 --> 00:04.965
for the non-life insurance companies.

00:04.965 --> 00:07.565
So for insurance companies, we have life insurance companies

00:07.565 --> 00:08.925
and non-life insurance companies.

00:08.925 --> 00:11.245
So non-life insurance companies are everything,

00:11.245 --> 00:13.125
which is not life insurance companies.

00:13.125 --> 00:15.725
So we can think of auto insurance, home insurance,

00:16.145 --> 00:17.485
and, and, and so on.

00:17.485 --> 00:20.045
Commercial insurance farm, et cetera.

00:20.265 --> 00:23.165
So the idea here is for lost reserves.

00:23.465 --> 00:27.965
The idea is to be able to kind of set aside some money,

00:28.035 --> 00:30.525
basically for future payments, right?

00:30.525 --> 00:33.605
Basically is for payments that are actually being paid,

00:33.905 --> 00:35.645
but not enough, not not settled,

00:36.185 --> 00:41.125
or also for, claims that actually occurred,

00:41.185 --> 00:42.285
but not reported.

00:42.625 --> 00:45.325
So all for those claims, the, the company needs

00:45.325 --> 00:47.645
to set aside some, reserves

00:47.865 --> 00:52.165
and also some capital to be able, basically to be, to pay,

00:52.185 --> 00:55.445
those kind of, payments for their,

00:55.445 --> 00:56.845
their claimants and policy holders.

00:57.305 --> 00:59.925
So what happens here in insurance companies also in

01:00.125 --> 01:03.285
practice, that we assume independence between risks.

01:03.425 --> 01:06.565
So I mentioned some kind of lines of business such as,

01:06.565 --> 01:08.925
auto insurance or also, or commercial.

01:09.385 --> 01:12.525
Uh, but in practice, while calculating the reserve

01:12.625 --> 01:15.525
or also kind of setting those risk capital,

01:16.185 --> 01:19.845
it is assumed that those risks are kind of independent.

01:19.955 --> 01:23.045
However, we could observe that there is kind

01:23.045 --> 01:25.565
of interdependency between those risks,

01:25.565 --> 01:28.525
which can be explained by, several factors.

01:28.905 --> 01:32.485
Uh, we can think, for example, of natural disasters,

01:32.485 --> 01:35.485
or pandemics that might actually,

01:36.185 --> 01:38.405
impact different risks at the same time,

01:38.405 --> 01:40.405
we could also think of legal,

01:40.405 --> 01:41.565
or regulatory changes,

01:41.855 --> 01:45.045
which also might affect different risks at the same time.

01:45.425 --> 01:48.045
And this should be, taken into account, not

01:48.045 --> 01:49.085
to mention operational risks

01:49.385 --> 01:53.245
or, even more timely now, the climate change, right?

01:53.265 --> 01:55.405
So with an increase, for example, in the frequency

01:55.425 --> 01:58.565
and severity, of weather, related, events.

01:58.985 --> 02:02.805
Um, lastly, I could also mention, at a granular level.

02:02.825 --> 02:05.165
So at this, what I mentioned now is more macro,

02:05.425 --> 02:07.245
but we could also think of micro level.

02:07.265 --> 02:10.085
So for example, the same person might be kind

02:10.085 --> 02:12.725
of have a tendency to basically kind

02:12.725 --> 02:16.285
of claim in several kind of, coverages, right?

02:16.285 --> 02:19.325
So they could actually claim, in, in, in home insurance,

02:19.385 --> 02:21.565
but also have a tendency to claim in auto insurance.

02:21.585 --> 02:23.765
And this will also can lead to a kind

02:23.765 --> 02:25.045
of a dependence between the risks.

02:25.345 --> 02:27.125
And this dependence has

02:27.125 --> 02:30.565
to be taken into account while basically calculating the

02:30.565 --> 02:32.045
reserve, for insurance company,

02:32.195 --> 02:34.765
basically model dependence between the risks.

02:35.455 --> 02:38.285
There are two schools of thought or two main mainstreams.

02:38.305 --> 02:41.845
Uh, basically, so we have the more multivariate multi

02:42.155 --> 02:45.845
reserve in, which assume, a non-prem model,

02:45.845 --> 02:47.685
which is basically distribution free,

02:48.015 --> 02:51.205
which are basically extensions of the,

02:51.205 --> 02:53.445
so-called chain ladder method, which is the kind

02:53.445 --> 02:55.485
of the benchmark, or the MAC model.

02:55.945 --> 02:58.725
Uh, so a lot of work had been done in literature,

02:58.785 --> 02:59.785
For doing that.

02:59.985 --> 03:03.725
And we have also the parametric approach, which is,

03:03.725 --> 03:08.005
basically mainly, based on caps, which is basically,

03:08.305 --> 03:11.965
one of the, most, powerful statistical tools

03:12.065 --> 03:13.765
to capture dependencies between risks.

03:14.185 --> 03:17.765
Uh, so caps, have been done a lot in, in the literature.

03:18.225 --> 03:22.245
And also, we do have, the, well, the sermon

03:22.385 --> 03:24.125
of family of distributions

03:24.125 --> 03:26.765
that also have been actually introduced to capture,

03:26.765 --> 03:28.005
dependencies between risks.

03:28.025 --> 03:29.965
So those are the tools. Okay?

03:30.305 --> 03:33.165
Uh, so the, the, the sermon of distribution,

03:33.235 --> 03:36.205
will basically has been proven to be more flexible,

03:36.305 --> 03:37.965
for example, than capitalist on high

03:37.985 --> 03:39.165
or higher triple capitalis.

03:39.425 --> 03:41.485
Uh, so in terms of tools, the sermon

03:41.545 --> 03:43.205
of distribution is a flexible tool.

03:43.545 --> 03:44.845
So now in terms of methods

03:44.985 --> 03:47.965
or methodologies, so to estimate dependence between risks,

03:48.345 --> 03:52.485
so with, again, mentioned two main, well streams

03:52.625 --> 03:53.685
or, approaches.

03:53.985 --> 03:57.805
So we have the, what we call the simultaneous approach,

03:57.805 --> 04:01.565
where we're actually going to estimate the dependence,

04:01.625 --> 04:03.965
factor or depends parameter at the same

04:03.965 --> 04:05.165
time as the marginal.

04:05.225 --> 04:09.085
So here we have, let's assume two risks, so X one and X two.

04:09.425 --> 04:12.165
So if you want to basically estimate the dependence

04:12.165 --> 04:14.245
between X one and X two, we're going

04:14.245 --> 04:16.205
to use a maximum likelihood summation.

04:16.505 --> 04:19.485
And we're going to have a simultaneous estimation

04:19.505 --> 04:20.525
of the marginals.

04:20.625 --> 04:23.645
By marginal, I mean the parameters for the risk X one

04:23.645 --> 04:25.565
and X two, but also the dependence

04:25.565 --> 04:26.805
parameter between the two.

04:27.185 --> 04:31.885
Uh, so the, the issue of doing that, so we have first

04:32.005 --> 04:33.925
of all, well, a lot of parameters,

04:34.615 --> 04:37.685
which actually can lead to over fitting, but also,

04:37.685 --> 04:40.565
and more importantly, sometimes a misestimating

04:40.565 --> 04:43.925
of the marginals can lead to a mis misestimating

04:44.025 --> 04:46.485
of the dependent structure and vice versa, right?

04:46.485 --> 04:49.325
So if you misestimate the dependent structure,

04:49.475 --> 04:52.845
this can also mis, misestimate the, the marginals.

04:53.265 --> 04:56.565
And if you misestimate the marginals, it means, it means

04:56.565 --> 04:58.165
that it'll actually have a mises

04:58.165 --> 04:59.365
estimation to the reserves, right?

04:59.365 --> 05:01.685
Because the reserves is based on the,

05:01.685 --> 05:03.405
parameters estimated on the marginals.

05:03.405 --> 05:07.645
So, so then comm's, the, a more robust way, a robust way

05:07.645 --> 05:10.365
to kind of estimate the, dependence,

05:10.515 --> 05:13.685
parameter is well based on the rank based method,

05:13.895 --> 05:18.085
which has been actually, brought, earlier

05:18.225 --> 05:19.485
to the literature,

05:19.485 --> 05:20.885
but has been actually introduced

05:20.885 --> 05:23.445
to the loss reserving context in, about 2016.

05:23.905 --> 05:27.085
Uh, so, which actually, proved

05:27.225 --> 05:30.285
to be more robust method to estimate dependence.

05:30.345 --> 05:33.645
So here in this paper, what we're doing, we're using a more,

05:33.645 --> 05:36.645
that more robust estimation, which is the rank based method,

05:36.865 --> 05:38.845
and combine it with the flexible family

05:38.865 --> 05:40.445
of distributions, which is the sarov.

05:40.665 --> 05:42.045
And then we use actually the two,

05:42.055 --> 05:44.805
which is we have a flexible tool, which is the sarov

05:44.905 --> 05:49.765
and the rob more robs, estimation, method,

05:49.775 --> 05:51.925
which is basically the, the rank based method.

05:52.185 --> 05:54.565
And then we use them actually in this paper,

05:54.585 --> 05:56.205
to estimate the dependence between the risks.

05:56.645 --> 06:00.045
I insisted on the flexibility on the salmon of distribution,

06:00.175 --> 06:03.485
which also provides close form expressions, which is,

06:03.645 --> 06:06.165
a very, interesting result, which is not always

06:06.405 --> 06:08.485
provided what the kaa, methodologies

06:09.065 --> 06:12.485
and the sarov distribution was basically used in various

06:12.495 --> 06:16.005
areas in for the first applications, interestingly,

06:16.105 --> 06:18.365
was more in the medical, medical area, right?

06:18.625 --> 06:21.765
Uh, so then here we're bringing it more to the, to the,

06:21.765 --> 06:22.845
reserve in context.

06:23.265 --> 06:24.685
Uh, so that's for the sarov.

06:24.945 --> 06:26.925
And then we also use the, well,

06:26.985 --> 06:28.485
the GRM for the marginals.

06:28.505 --> 06:29.885
So the generalized, the neuro models.

06:30.305 --> 06:34.445
Uh, so here the cover rates when we work with lost reserve.

06:35.345 --> 06:37.645
So when we work with actually lost triangles,

06:37.825 --> 06:41.765
the cover rates or explanatory variables would be basically

06:42.145 --> 06:43.205
the accident years.

06:43.425 --> 06:46.525
So the rows, so that would be, cover rates

06:46.545 --> 06:47.965
and also the development period.

06:48.025 --> 06:50.525
So the column, so, so this is basically the cover rates

06:50.525 --> 06:53.045
that we use, for the lost triangle.

06:53.505 --> 06:57.325
And what happens is for this methodology, so we, first,

06:57.675 --> 06:59.125
it's a two step inference, right?

06:59.125 --> 07:00.925
So it's a two stage inference method.

07:01.225 --> 07:04.085
So first we estimate the marginals, okay?

07:04.105 --> 07:06.285
And then we get the parameters for the marginals.

07:06.595 --> 07:10.805
From there, we calculate the ILS right from those,

07:11.365 --> 07:13.285
marginals obtained by the GM.

07:13.615 --> 07:16.205
After that, we calculate their rank of renewals,

07:16.625 --> 07:19.605
and then we actually use the, so the likelihood

07:19.785 --> 07:23.245
to calculate, well, of course, using those rank of renewals

07:23.425 --> 07:26.325
to, calculate the dependence parameter of the summon

07:26.325 --> 07:29.605
of distribution for both bate or tra triver it.

07:29.665 --> 07:34.005
So also, one of the, nice feature of the, of the,

07:34.065 --> 07:36.445
of the model is it's easily extendable to,

07:36.625 --> 07:37.805
we could easily extend it

07:37.805 --> 07:39.165
to more than two lines of business.

07:39.165 --> 07:42.005
So we use that for three risks, for example,

07:42.065 --> 07:43.565
but that could be easily extended

07:43.585 --> 07:45.125
to more than, three risks.

07:45.385 --> 07:49.725
So in terms of the main results, so we actually applied,

07:49.905 --> 07:52.405
our methodologies to seven lines

07:52.405 --> 07:57.285
of business from a real dataset, from, both a major us,

07:57.465 --> 07:59.285
property and casualty insurance company,

07:59.305 --> 08:02.205
but also a large Canadian, insurance company.

08:02.745 --> 08:05.885
And the results were really consistent in a way.

08:05.885 --> 08:07.845
So two things in particular.

08:08.145 --> 08:11.365
So the first thing is all the kind of,

08:11.475 --> 08:13.725
rank based mol method are proved

08:13.725 --> 08:15.885
to actually better capture the dependence than

08:15.885 --> 08:16.965
the one stage inference.

08:17.145 --> 08:19.845
So recall when I actually mentioned those,

08:19.905 --> 08:21.085
two types of summations.

08:21.085 --> 08:22.165
So the simultaneous one,

08:22.225 --> 08:25.485
the one one step inference versus the rank based method,

08:25.565 --> 08:26.925
which is caught up a two step.

08:27.225 --> 08:30.645
So the two step or two stage inference basically captured

08:30.665 --> 08:33.165
better the dependence than the one step inference.

08:33.165 --> 08:36.085
So for example, if I give you a line of business,

08:36.085 --> 08:37.645
let's say one and two,

08:37.865 --> 08:40.005
and we use the approach classical approach one,

08:40.005 --> 08:43.325
which is the one step inference, it did actually, fail

08:43.385 --> 08:44.605
to capture the dependence.

08:44.605 --> 08:45.765
So basically what means

08:45.765 --> 08:48.645
that the dependence is not significant if we use that.

08:48.945 --> 08:51.085
But when we actually model the dependence

08:51.085 --> 08:53.565
between this very same lines of business one

08:53.565 --> 08:55.405
and two, using the two stage inference,

08:55.785 --> 08:58.485
we were able actually to kind of capture the dependence

08:58.485 --> 09:01.925
and the de de dependence ended up being, significant.

09:02.025 --> 09:03.765
So that's the first, finding.

09:04.225 --> 09:07.965
The second finding, earlier I was discussing,

09:08.145 --> 09:09.645
for the insurance company.

09:09.745 --> 09:12.365
So of course, the insurance company has an inverted

09:12.455 --> 09:13.725
production cycle, right?

09:13.905 --> 09:16.365
So the idea, because, what I was mentioning earlier

09:16.945 --> 09:21.725
is basically we, receive, the, the, the, the,

09:21.725 --> 09:25.165
the, the, actually the, the, the, the, the, the price

09:25.225 --> 09:26.405
before knowing the cost.

09:26.465 --> 09:28.245
So the price is the premium

09:28.505 --> 09:30.965
before knowing the cost, which is basically the claim.

09:31.065 --> 09:34.125
So the insurance company has actually to estimate

09:34.475 --> 09:36.845
what is the cost, and then after,

09:37.175 --> 09:40.165
after that, basically estimating, the price of that.

09:40.265 --> 09:43.325
So this is interesting for the insurance production cycle,

09:43.325 --> 09:45.485
because it is inverted, unlike most

09:45.505 --> 09:48.765
of the other production cycles, if we are selling a shoe,

09:48.765 --> 09:51.565
for example, we know exactly how much it did cost us, right?

09:51.665 --> 09:53.245
So, and then in addition to that,

09:53.265 --> 09:55.525
we calculate the profit, and then we have the price.

09:55.585 --> 09:57.005
So here it's inverted.

09:57.345 --> 09:59.485
So we need to calculate that risk,

09:59.705 --> 10:03.445
but also have a kind of an expected fall, which is a kind

10:03.445 --> 10:06.405
of a, a buffer for adverse scenarios.

10:06.405 --> 10:08.885
So, and for that, we need to calculate,

10:09.005 --> 10:10.845
risk measures measure, on also

10:10.845 --> 10:12.125
what we call the risk capital.

10:12.785 --> 10:17.365
And the method we suggested, proved that we actually

10:17.985 --> 10:20.205
are able to reduce that risk capital.

10:20.385 --> 10:23.765
So we, we reduce the risk capital using the rank based,

10:23.765 --> 10:24.845
multi-grade mov.

10:25.145 --> 10:27.845
And this has a direct consequence

10:27.905 --> 10:29.245
for the insurance companies

10:29.245 --> 10:30.805
because it actually,

10:30.805 --> 10:33.205
provides a better diversification benefits, right?

10:33.205 --> 10:36.045
So we have more gains in terms of the risk capital,

10:36.295 --> 10:39.445
which is, a tangible, consequence here

10:39.505 --> 10:40.645
for the insurance industry.

10:40.985 --> 10:42.725
We proved that the, the,

10:42.745 --> 10:46.645
the proposed model outperformed classical models,

10:46.705 --> 10:49.725
for both capture and dependence between the risks,

10:50.025 --> 10:52.485
and also in terms of providing, a,

10:52.645 --> 10:54.405
a greater diversification benefit.

10:54.705 --> 10:58.285
So that's, a, a very important, result.

10:58.585 --> 11:00.805
Uh, of course, each work can be

11:01.045 --> 11:02.245
extended and can be improved.

11:02.665 --> 11:05.805
Uh, so here we discussed two step inference.

11:05.865 --> 11:07.645
So one step was for the marginals.

11:07.905 --> 11:11.605
So we could basically, improve, the, for the,

11:11.605 --> 11:15.245
the marginals here we could, for example, so we use the GLM,

11:15.345 --> 11:17.805
but we could also use, use for example, generalized,

11:17.835 --> 11:19.005
partial linear models

11:19.065 --> 11:22.005
or the GPLM, which incorporates both linear

11:22.105 --> 11:23.245
and nonlinear components.

11:23.465 --> 11:25.765
So that could basically,

11:25.875 --> 11:27.805
improve the result for the marginals.

11:28.105 --> 11:30.365
Uh, and same for the dependent structure.

11:30.425 --> 11:34.125
So we could also think, for example, we use here the OV for,

11:34.545 --> 11:35.765
aggregated data,

11:36.025 --> 11:38.845
but we could also think, for example, to extend it

11:38.845 --> 11:40.005
to granular data.

11:40.145 --> 11:41.965
So here, which is basically instead

11:42.125 --> 11:46.325
of having a lost triangle, instead of having basically,

11:46.465 --> 11:49.165
to capture dependence between two lines

11:49.165 --> 11:50.205
of business, right?

11:50.345 --> 11:52.725
So using aggregate data, so we could basically

11:52.745 --> 11:55.165
Use it for individual data, right?

11:55.225 --> 11:59.445
So here we could, access more granular, information,

11:59.515 --> 12:00.725
more detailed information.

12:01.065 --> 12:03.805
And this also could reduce, overfitting

12:03.805 --> 12:06.165
because we have, access

12:06.225 --> 12:08.165
to more information enhanced more data.

12:08.545 --> 12:11.165
And of course, last

12:11.185 --> 12:14.245
but not least, for industry professionals,

12:14.315 --> 12:16.405
this is a very important,

12:16.405 --> 12:19.325
because we want the resource as well to be applicable,

12:19.585 --> 12:22.125
and, applied also in the industry.

12:22.545 --> 12:25.605
And one of the, benefits is that the,

12:25.605 --> 12:29.285
these model can be very valuable resource for the property

12:29.285 --> 12:30.805
and casualty insurance companies.

12:31.225 --> 12:33.445
Uh, and especially now with,

12:33.505 --> 12:37.965
the International Financial Reporting standards IFRS 17,

12:37.965 --> 12:39.245
this could be a very good tool

12:39.265 --> 12:42.765
to aid them in meeting those IRS 17, regulations.

12:43.065 --> 12:45.725
And also, of course, while, enhancing their,

12:45.725 --> 12:47.165
solvency risk assessment.

12:47.345 --> 12:50.165
And if this actually happens,

12:50.165 --> 12:53.685
this is actually very beneficial for the, economy,

12:53.785 --> 12:54.925
but also for the society,

12:54.925 --> 12:57.205
because it'll have a positive, economic

12:57.265 --> 13:00.645
and societal impact, by improving the insurance company.

13:00.985 --> 13:03.165
Uh, so solvency ratio.

Understanding Loss Reserves in Non-Life Insurance

00:00:00 - So this is the context and the, loss reserve for the non-life insurance companies. So for insurance companies, we have life insurance companies and non-life insurance companies. So non-life insurance companies are everything, which is not life insurance companies. So we can think of auto insurance, home insurance, and, and, and so on. Commercial insurance farm, et cetera. So the idea here is for lost reserves. The idea is to be able to kind of set aside some money, basically for future payments, right?
00:00:33 - but not enough, not not settled, or also for, claims that actually occurred, but not reported. So all for those claims, the, the company needs to set aside some, reserves and also some capital to be able, basically to be, to pay, those kind of, payments for their, their claimants and policy holders. So what happens here in insurance companies also in practice, that we assume independence between risks.
00:01:06 - auto insurance or also, or commercial. but in practice, while calculating the reserve or also kind of setting those risk capital, it is assumed that those risks are kind of independent. However, we could observe that there is kind of interdependency between those risks, which can be explained by, several factors. we can think, for example, of natural disasters, or pandemics that might actually,
00:01:38 - we could also think of legal, or regulatory changes, which also might affect different risks at the same time. And this should be, taken into account, not to mention operational risks or, even more timely now, the climate change, right? So with an increase, for example, in the frequency and severity, of weather, related, events. lastly, I could also mention, at a granular level. So at this, what I mentioned now is more macro, but we could also think of micro level.
00:02:10 - of have a tendency to basically kind of claim in several kind of, coverages, right? So they could actually claim, in, in, in home insurance, but also have a tendency to claim in auto insurance. And this will also can lead to a kind of a dependence between the risks. And this dependence has to be taken into account while basically calculating the reserve, for insurance company, basically model dependence between the risks. There are two schools of thought or two main mainstreams.
00:02:42 - reserve in, which assume, a non-prem model, which is basically distribution free, which are basically extensions of the, so-called chain ladder method, which is the kind of the benchmark, or the MAC model. so a lot of work had been done in literature, For doing that. And we have also the parametric approach, which is, basically mainly, based on caps, which is basically,

Estimating Risk Dependencies Using Robust Methods

00:03:12 - to capture dependencies between risks. so caps, have been done a lot in, in the literature. And also, we do have, the, well, the sermon of family of distributions that also have been actually introduced to capture, dependencies between risks. So those are the tools. Okay? so the, the, the sermon of distribution, will basically has been proven to be more flexible, for example, than capitalist on high or higher triple capitalis.
00:03:41 - of distribution is a flexible tool. So now in terms of methods or methodologies, so to estimate dependence between risks, so with, again, mentioned two main, well streams or, approaches. So we have the, what we call the simultaneous approach, where we're actually going to estimate the dependence, factor or depends parameter at the same time as the marginal. So here we have, let's assume two risks, so X one and X two.
00:04:12 - between X one and X two, we're going to use a maximum likelihood summation. And we're going to have a simultaneous estimation of the marginals. By marginal, I mean the parameters for the risk X one and X two, but also the dependence parameter between the two. so the, the issue of doing that, so we have first of all, well, a lot of parameters, which actually can lead to over fitting, but also, and more importantly, sometimes a misestimating
00:04:44 - of the dependent structure and vice versa, right? So if you misestimate the dependent structure, this can also mis, misestimate the, the marginals. And if you misestimate the marginals, it means, it means that it'll actually have a mises estimation to the reserves, right? Because the reserves is based on the, parameters estimated on the marginals. So, so then comm's, the, a more robust way, a robust way to kind of estimate the, dependence, parameter is well based on the rank based method,
00:05:18 - to the literature, but has been actually introduced to the loss reserving context in, about 2016. so, which actually, proved to be more robust method to estimate dependence. So here in this paper, what we're doing, we're using a more, that more robust estimation, which is the rank based method, and combine it with the flexible family of distributions, which is the sarov. And then we use actually the two, which is we have a flexible tool, which is the sarov
00:05:49 - which is basically the, the rank based method. And then we use them actually in this paper, to estimate the dependence between the risks. I insisted on the flexibility on the salmon of distribution, which also provides close form expressions, which is, a very, interesting result, which is not always provided what the kaa, methodologies and the sarov distribution was basically used in various areas in for the first applications, interestingly,

Improving Loss Reserves with Advanced Modeling Techniques

00:06:18 - so then here we're bringing it more to the, to the, reserve in context. so that's for the sarov. And then we also use the, well, the GRM for the marginals. So the generalized, the neuro models. so here the cover rates when we work with lost reserve. So when we work with actually lost triangles, the cover rates or explanatory variables would be basically the accident years. So the rows, so that would be, cover rates
00:06:48 - So the column, so, so this is basically the cover rates that we use, for the lost triangle. And what happens is for this methodology, so we, first, it's a two step inference, right? So it's a two stage inference method. So first we estimate the marginals, okay? And then we get the parameters for the marginals. From there, we calculate the ILS right from those, marginals obtained by the GM. After that, we calculate their rank of renewals,
00:07:19 - to calculate, well, of course, using those rank of renewals to, calculate the dependence parameter of the summon of distribution for both bate or tra triver it. So also, one of the, nice feature of the, of the, of the model is it's easily extendable to, we could easily extend it to more than two lines of business. So we use that for three risks, for example, but that could be easily extended to more than, three risks. So in terms of the main results, so we actually applied,
00:07:52 - of business from a real dataset, from, both a major us, property and casualty insurance company, but also a large Canadian, insurance company. And the results were really consistent in a way. So two things in particular. So the first thing is all the kind of, rank based mol method are proved to actually better capture the dependence than the one stage inference. So recall when I actually mentioned those,
00:08:21 - So the simultaneous one, the one one step inference versus the rank based method, which is caught up a two step. So the two step or two stage inference basically captured better the dependence than the one step inference. So for example, if I give you a line of business, let's say one and two, and we use the approach classical approach one, which is the one step inference, it did actually, fail to capture the dependence. So basically what means that the dependence is not significant if we use that. But when we actually model the dependence
00:08:53 - and two, using the two stage inference, we were able actually to kind of capture the dependence and the de de dependence ended up being, significant. So that's the first, finding. The second finding, earlier I was discussing, for the insurance company. So of course, the insurance company has an inverted production cycle, right? So the idea, because, what I was mentioning earlier is basically we, receive, the, the, the, the,

Inverted Production Cycle in Insurance

00:09:25 - before knowing the cost. So the price is the premium before knowing the cost, which is basically the claim. So the insurance company has actually to estimate what is the cost, and then after, after that, basically estimating, the price of that. So this is interesting for the insurance production cycle, because it is inverted, unlike most of the other production cycles, if we are selling a shoe, for example, we know exactly how much it did cost us, right? So, and then in addition to that,
00:09:55 - So here it's inverted. So we need to calculate that risk, but also have a kind of an expected fall, which is a kind of a, a buffer for adverse scenarios. So, and for that, we need to calculate, risk measures measure, on also what we call the risk capital. And the method we suggested, proved that we actually are able to reduce that risk capital. So we, we reduce the risk capital using the rank based,
00:10:25 - And this has a direct consequence for the insurance companies because it actually, provides a better diversification benefits, right? So we have more gains in terms of the risk capital, which is, a tangible, consequence here for the insurance industry. We proved that the, the, the proposed model outperformed classical models, for both capture and dependence between the risks, and also in terms of providing, a, a greater diversification benefit.
00:10:58 - of course, each work can be extended and can be improved. so here we discussed two step inference. So one step was for the marginals. So we could basically, improve, the, for the, the marginals here we could, for example, so we use the GLM, but we could also use, use for example, generalized, partial linear models or the GPLM, which incorporates both linear and nonlinear components. So that could basically,
00:11:28 - and same for the dependent structure. So we could also think, for example, we use here the OV for, aggregated data, but we could also think, for example, to extend it to granular data. So here, which is basically instead of having a lost triangle, instead of having basically, to capture dependence between two lines of business, right? So using aggregate data, so we could basically Use it for individual data, right? So here we could, access more granular, information,
00:12:01 - And this also could reduce, overfitting because we have, access to more information enhanced more data. And of course, last but not least, for industry professionals, this is a very important, because we want the resource as well to be applicable, and, applied also in the industry. And one of the, benefits is that the, these model can be very valuable resource for the property and casualty insurance companies.

Enhancing Solvency Through IFRS 17 Compliance

00:13:00 - the International Financial Reporting standards IFRS 17, this could be a very good tool to aid them in meeting those IRS 17, regulations. And also, of course, while, enhancing their, solvency risk assessment. And if this actually happens, this is actually very beneficial for the, economy, but also for the society, because it'll have a positive, economic and societal impact, by improving the insurance company. so solvency ratio.

Faculti AI can make mistakes

Faculti

Popular in Sciences

Diameter rigidity for Kähler manifolds with positive bisectional curvature

Plasticity and microevolution of diatoms

Statistical Mechanics for Chemistry and Materials Science

Polyfluorene-Wrapped Carbon Nanotubes Decorated with Photocleavable Side-Chains

Analysis of rare coding variants reveals novel genetic risk factors for type 2 diabetes

The Mouse Cortical Connectome Maintains Specificity by Distinct Connectivity Profiles

The Hybrid High-Order Method for Polytopal Meshes

Rank-Based Multivariate Sarmanov for Modeling Dependence

Next in Formal Sciences

Guide

Platform and Category Pages

Contact Us

FAQs

What is Faculti?

How do you select interviews?

Interview Process

Page Structure

Popular in Sciences

Guide

Platform and Category Pages

Contact Us

FAQs

What is Faculti?

How do you select interviews?

Interview Process

Accessibility Options

Contrast Adjustment

Text Size Adjustment

Text Spacing Adjustment

Line Height Adjustment

Cursor Size Adjustment

Page Structure Options

Page Structure