After working on a bootstrapping framework for the Mack model, with a one-year point of view and with several triangles to bootstrap jointly, i decided to put some of my code into a litle package, mbmcl.
You can install it with :
We’ll also load some conveniance packages, namely magrittr/dplyr/purrr/tibble/tidyr.
library(magrittr)
library(dplyr)
library(purrr)
library(tibble)
library(tidyr)
Then load some triangle data, for exemple the ABC triangle from the ChainLadder package. For the purpose of this exposition, we need several triangles of same size, lets create dummy triangles, and look at mack’s results on them :

My actuarial thesis got published online there
This work took me a little more than one year to do, an was dealing with non-life reserving in solvency 2 context for the french decenial insurance contracts. Here’s the abstract :
After having specified the specificities of the French builder’s insurance and analyzed the problems posed by additional specific reserves to this line of buisiness, we recall basic models, deterministic and stochastic, used in non-life insurance.

Introduction
Suppose you have a dataset, and you are narowing possible machine learning models to 2 or 3 models, but you still cant choose which you want : Will the benefit of understandability from my CART cost me too much compare to a random forest or some bootsting ?
Well you dont necessarily have to choose : juste agregate the models you have to make a better one. Typicaly, if you have models that dont uses the same features of the dataset, or give very different ansewrs but are still all good in term of a pre-selected metric (let’s say RMSE for regression, area under ROC for classification), ensembling them could be a good idea.

Introduction
The log-normal model
Generating dummy dataset.
Checking model hypohtesis.
Log-normality of \(y_t\)
Linearity between \(y_t\) and \(x_t\)
Results from the model
References
Introduction
Under Solvency 2 framework, insurance compagnies can calculate undertaking specific parameters to modify their application of the standard formula, as dictates Commission-Européenne (2014) . One of thoose calculations methods uses a log-normal model that’s quite interessante to analyse. We will here analyse this model in a mathematical sense, and then use it on simulated data (i’m not an insurence compagny !

Which actuary does not know about Mack’s model ? Due to Mack (1991), this model is fairly simple. Suppose you have a triangle.
Ok seeing the origin dates of claims, thoose data are old. But who cares ? Let’s denote \(C_{i,j}\) the value of this triangle from the \(i\)’th row and the \(j\)’th collumn.
The mack model consist of a stochastic model that enframe the classical chain-ladder estimator, denoted here by the vector \(\mathbf{\hat{f}}\), defined \(\forall j \in \{1,.

Introduction
Le modèle de vasicek et quelques pré-requis
Le modèle de Hull et White
Simulations
Simulation du taux court
Simulation du prix du zéro-coupon \(B(0,T)\)
Simulation et graphe de la courbe de taux
Conclusion
Annexes
Introduction
Disclaimer : this is the summary of a project done with 2 friends for Pr Jiao Ying in 2017. The corresponding code is avaliable here. Sorry but the following is in french.