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Old 09-10-2019, 08:07 AM
sociosalato sociosalato is offline
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Join Date: Sep 2013
College: UniversitÓ Cattolica del Sacro Cuore di Milano
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Default Normal Distributions and Life Risks (SII)

Hi erverybody,

I hope you can help me to figure out my doubt.
About 1 month ago I had an interview (i'll keep it anonymous) during which the interviewer asked me to give him an example of a life risk (Solvency II) not really normally ditributed.

Intuitively I told him that Mortality risk distribution may not follow a normal distribution, giving him my reasons.
I later found EIOPA underlining it here (page 31) https://eiopa.europa.eu/Publications...ssumptions.pdf).

He answered me that that mortality was not really that far from a Normal Distribution and that the right answer was Morbidity, because of its manifestation along the years: these events usually happen every X years.

Now, I have no doubts about the accuracy and technical knowledge of the interviewer (I trust his answer and have great respect of his background), but I'm not fully understanding the connection between normality and timing manifestation of the morbidity event. Can anybody enlight me?

Thank you everybody
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Old 09-10-2019, 08:21 AM
The_Polymath The_Polymath is offline
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Join Date: Jun 2016
Posts: 3,157
Default

Quote:
Originally Posted by sociosalato View Post
Hi erverybody,

I hope you can help me to figure out my doubt.
About 1 month ago I had an interview (i'll keep it anonymous) during which the interviewer asked me to give him an example of a life risk (Solvency II) not really normally ditributed.

Intuitively I told him that Mortality risk distribution may not follow a normal distribution, giving him my reasons.
I later found EIOPA underlining it here (page 31) https://eiopa.europa.eu/Publications...ssumptions.pdf).

He answered me that that mortality was not really that far from a Normal Distribution and that the right answer was Morbidity, because of its manifestation along the years: these events usually happen every X years.

Now, I have no doubts about the accuracy and technical knowledge of the interviewer (I trust his answer and have great respect of his background), but I'm not fully understanding the connection between normality and timing manifestation of the morbidity event. Can anybody enlight me?

Thank you everybody
He's right about mortality.

I have designed internal models for SII, and mortality is a small life risk, and usually modelled using a normal distribution. There is not much point in using a more computationally complex distribution given how little tail activity there is.

A better example would have been longevity risk. This risk is composed of base parameter risk (also usually modelled using a normal distribution), and trend risk (this one is the best example of a non-normal distribution).

Longevity trend risk is one of the biggest capital risks for life insurers, and the complexity of the modelling involved reflects this.
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