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  #11  
Old 05-07-2019, 04:54 AM
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The_Polymath The_Polymath is offline
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Originally Posted by Glenn Meyers View Post
This was a hot topic in the mid 2000's. I gave a presentation on it at the 2005 CAS Ratemaking Seminar. The link to download the presentation is below -- 2nd one down in the "Presentations" tab.

The general idea is to use a collective risk model to calculate the amount of capital the company needs with, and without the reinsurance. Then compare the cost of capital without reinsurance, with the cost of capital with the reinsurance plus the margin charged by the reinsurer.

One complication is that you need to address how long you need to hold capital for long-tailed lines. I have an upcoming Variance paper on that addresses the problem from the Solvency II perspective. It does not address the reinsurance problem. It should be out any day now. The presentation linked below should give one a feel for the problem for reinsurance

The general result that jumped out of a number of analyses that I did back then was that for all but the fairly small insurers, one should not buy reinsurance for liability lines of insurance. But one should buy reinsurance for catastrophes. My caveat is that cost of capital is your sole consideration for buying reinsurance.

https://www.casact.org/education/ind...&submit=Search
Cool. Thanks Glenn. From reading the ppt, there are a few areas I will post later in as I am in the process of sketching out the model structure.
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  #12  
Old 05-07-2019, 09:38 AM
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Originally Posted by Glenn Meyers View Post
Yeah, I made a lot of presentations that year. The one you referenced was the 4th one down. Look at the 2nd one above that on the same page that the link takes you to.
Ya, but, read the title again.
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  #13  
Old 05-07-2019, 10:02 AM
Glenn Meyers Glenn Meyers is offline
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The CAS seems to think you gave a talk on Generalized Addictive Models, btw.

The slip may have been more Freudian than typo. Models can be addictive --- especially your own models. Withdrawal can be traumatic, but it gets easier with time and experience.
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  #14  
Old 05-08-2019, 08:24 AM
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Quote:
Originally Posted by Glenn Meyers View Post
This was a hot topic in the mid 2000's. I gave a presentation on it at the 2005 CAS Ratemaking Seminar. The link to download the presentation is below -- 2nd one down in the "Presentations" tab.

The general idea is to use a collective risk model to calculate the amount of capital the company needs with, and without the reinsurance. Then compare the cost of capital without reinsurance, with the cost of capital with the reinsurance plus the margin charged by the reinsurer.

One complication is that you need to address how long you need to hold capital for long-tailed lines. I have an upcoming Variance paper on that addresses the problem from the Solvency II perspective. It does not address the reinsurance problem. It should be out any day now. The presentation linked below should give one a feel for the problem for reinsurance

The general result that jumped out of a number of analyses that I did back then was that for all but the fairly small insurers, one should not buy reinsurance for liability lines of insurance. But one should buy reinsurance for catastrophes. My caveat is that cost of capital is your sole consideration for buying reinsurance.

https://www.casact.org/education/ind...&submit=Search
Agreed on CoC approach. It gets hard though when you have international exposures for large commercial properties, as then you have different large loss distributions per country (or location), which can then have reinsurers in multiple countries, with recoverables in different currencies (so FX risk), that all correlate together, to arrive at an aggregate cost of capital for the reinsurance strategy in general. This then also needs to be adjusted for credit risk as well.

It's messy. Just trying to think of a way of simplifying it so that the model is easier to use.
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  #15  
Old 05-08-2019, 09:40 AM
Glenn Meyers Glenn Meyers is offline
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Originally Posted by The_Polymath View Post
Agreed on CoC approach. It gets hard though when you have international exposures for large commercial properties, as then you have different large loss distributions per country (or location), which can then have reinsurers in multiple countries, with recoverables in different currencies (so FX risk), that all correlate together, to arrive at an aggregate cost of capital for the reinsurance strategy in general. This then also needs to be adjusted for credit risk as well.

It's messy. Just trying to think of a way of simplifying it so that the model is easier to use.
Below is a link to the "Articles in Press" version of my cost of capital paper that should be up in Variance shortly. The data required are loss triangles, and I was thinking Solvency II when I wrote this paper. Thinking of reinsurance, one way to do it is to assemble loss triangles under various reinsurance assumptions and proceed as described in this paper.

https://www.variancejournal.org/arti...ies-Meyers.pdf

I was working at ISO at the time when I wrote a series of paper on financing insurance. We had loss distributions by line of business and by development period. We tried to make the "Cost of Financing" idea into a product. But we could not get enough sales to keep it going.

If I were doing this now in an insurance company environment, I think I would use the assembling loss triangles approach as opposed to the collective risk model approach.
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  #16  
Old 05-08-2019, 11:15 AM
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Originally Posted by tommie frazier View Post
large broker firm would have analytics team to assist with this for sure.

This is no doubt true. The 3 big reinsurance brokers each have their own model. But in some sense, this is like asking the diamond merchant how much you should spend on a diamond. I may be a cynic, but I believe the result of the model is skewed to favor more purchases, and purchases in the brokers' most profitable lines (i.e. CAT)
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  #17  
Old 05-09-2019, 09:22 AM
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Quote:
Originally Posted by Glenn Meyers View Post
Below is a link to the "Articles in Press" version of my cost of capital paper that should be up in Variance shortly. The data required are loss triangles, and I was thinking Solvency II when I wrote this paper. Thinking of reinsurance, one way to do it is to assemble loss triangles under various reinsurance assumptions and proceed as described in this paper.

https://www.variancejournal.org/arti...ies-Meyers.pdf

I was working at ISO at the time when I wrote a series of paper on financing insurance. We had loss distributions by line of business and by development period. We tried to make the "Cost of Financing" idea into a product. But we could not get enough sales to keep it going.

If I were doing this now in an insurance company environment, I think I would use the assembling loss triangles approach as opposed to the collective risk model approach.
Glenn - this shift in your perspective is intriguing; are you willing to elucidate?
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  #18  
Old 05-09-2019, 05:36 PM
Glenn Meyers Glenn Meyers is offline
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My thinking on financing insurance has been evolving for almost all of my actuarial career. At last November’s CAS meeting I attempted to describe this evolution. Here is the link to my presentation.

https://www.casact.org/education/ann...ations/C-1.pdf

There were two considerations that led me from the collective risk model approach dating from around 2000, to the stochastic loss reserving approach I suggested trying in my previous post. They were ease of implementation and ease of gaining acceptance.

Implementation first --- The collective risk model approach involved fitting a lot of severity distribution and making educated guesses (with some modeling assistance) of contagion parameters and correlations. As I gave presentations (sales pitches) to a number of insurers, I sensed significant unease with the number of estimates, from external data, that we had to string together. In short, the collective risk model approach was a “bleeding edge” approach.

By contrast, as I showed in my recent risk margin paper, if you have a loss triangle, and can agree on some rates of return, you can calculate a risk margin for a line of insurance in minutes. There should be some discussion on how to combine lines, but I will say that the dependency problem is overrated. If you have a dependency problem, the real problem is the model selection problem.

As for reinsurance optimization, if you have good claims IT support, you should be able to construct loss triangles for a variety of proposed reinsurance programs. It then becomes a matter of comparing the cost of capital for the various reinsurance proposals.

Now acceptance --- As my day job moved on to predictive modeling, in my extracurricular activities I got a chance to watch the development of Solvency II, IFRS 17 and related initiatives through my IAA/ASTIN participation. There I saw a growing acceptance of capital modeling and parallels between my thinking and others on cost of capital risk margins. The weak point in all of this was getting a distribution of capital cash flows.

Enter Bayesian MCMC ---- As I was nearing retirement I, with the help of others, managed to get set up the CAS Loss Reserve Database. Also, I was able to latch onto Bayesian MCMC as it was beginning to mature.

So I began my little retirement project. Bayesian MCMC is ideal for stochastic loss reserving. My sense is that it has yet to gain mainstream acceptance for loss reserving, but I like its trajectory.

Bayesian MCMC will give you a lot (10,000) of equally likely cash flows for risk margin calculations.

There is one thing I want to make clear --- I never considered stochastic loss reserve modeling to be the end product. I was always after the risk margin.
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  #19  
Old 05-12-2019, 10:38 PM
Harbinger Harbinger is offline
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Subscribe. Great thread so far. Reading Glenn’s MCMC paper is on my to-do list. A co-worker of mine implemented Glenn’s changing settlement rate method and I need to better understand how it works.
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  #20  
Old 05-13-2019, 12:31 PM
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Klaymen Klaymen is offline
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Maybe it should be Generalized Addictive Morels
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