The making of a shiny mauc
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When an excess of loss (XOL) reinsurance pricing actuary has only indemnity to work with, how can s/he reflect allocated loss adjustment expense (ALAE) in final cost projections? Such is the situation addressed by Greg McNulty in his blog Modeling ALAE Using Copulas (MAUC). According to McNulty, the classical approach — loading the indemnity value of each claim with an average ALAE/indemnity ratio — rests on “two very strong implicit assumptions”: 1) ALAE and indemnity are “scaled copies” of each other and 2) ALAE and indemnity are “100% correlated.” When those assumptions are questionable McNulty suggests an alternative approach.
From a different dataset of (indemnity, ALAE) pairs, McNulty fits a marginal distribution to the ALAE and a copula distribution to the joint pairs. He then marries the original indemnity to the fitted ALAE using the presiding copula. The result is a bivariate distribution of indemnity and ALAE which
From a different dataset of (indemnity, ALAE) pairs, McNulty fits a marginal distribution to the ALAE and a copula distribution to the joint pairs. He then marries the original indemnity to the fitted ALAE using the presiding copula. The result is a bivariate distribution of indemnity and ALAE which
- maintains the shape of the original indemnity,
- reflects its expected interaction with ALAE throughout their combined domain, and
- can be used to simulate risk-adjusted pricing for XOL layers of interest and under the two standard treatments of ALAE.
McNulty provides the supporting R code to implement all his algorithms and reproduce all his results! With this paper Greg takes his place in the evolution of Reproducible Research (see 1 and 2 and even 3) within the research arm of my professional organization.
A more thorough discussion of the actuarial content of McNulty’s paper is not the purpose of this blog. This blog will be much more geeky! Over the coming weeks we will walk through the steps that will turn McNulty’s code into an online shiny app. Once online, his code can be run by virtually anyone. No need to install R or any of the required packages. All that’s needed is a browser. That way, non-R-conversant actuaries will be able to reproduce McNulty’s results, hopefully leading to a deeper appreciation of his concepts. An enhanced version of the app that could run the calculations on your own data would probably lead to an even deeper appreciation, but let’s not get ahead of ourselves!
For the purpose of this exercise Greg has generously granted his permission for his code to be shared online in a github public repository (anyone can view the site and all its content). You can find the MAUC repository here.
Cheers to you, Greg, for providing this solution and software, and to the Casualty Actuarial Society and its Open-SourceSoftware Committee for supporting his work.
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