STA2453 Project 2 - Insurance Company Solution

You are starting your own Canadian insurance company from data you recently acquired at auction from a now-defunct commercial insurance company called AFC Industries.
AFC industries holds market data on several commercial business clients in the GTA. There are two data sets to consider. The claims data under the name AFC_claims.csv, and their policy data AFC_policies.csv.
Your job is to create a premium model and attempt to acquire new clients listed under the name of potential_clients.csv.
Loss-Cost Model
The essence of insurance pricing comes down to the loss-cost model. The premium cost is unique for every commercial building client.
The equation for calculating a premium is as follows:
Premium = Cost + Profit
I.e. we are interested in modelling the cost, and then determining the margin of profit. We seek to have the client both pay their cost, and, contribute to our company profit.
The cost can be separated into multiple sub-components denoted as the following:
Expected Losses (Claims from the client)
Loss Adjustment Expenses Underwriting Expenses
This results in the following formula:
Premium = Expected Losses + Loss Adjustment Expenses + Underwriting Expenses
These components can be broken down further, however, we are going to use the pure premium method to calculate premiums as written in Chapter 8 of Werner & Modlin.
$$ PurePremium = rac{ExpectedLoss * (1 + LossAllocatedExpenses) + FixedExpensesPerPolicy}{1 - VariableExpensesPerPolicy ProfitLoading} $$
$ ExpectedLoss $ the amount of loss the targeted client is predicted to occur.
$ FixedExpensesPerPolicy $ day-to-day running expenses for facilitating insurance coverage overall. Commercial rent, server costs, etc.
$ ProfitLoading $, similar to a profit margin; you as an executive, get to determine on how much to charge your customers.
Note that you can consolidate the last two variables of interest for the pure premium into one number, ultimately these are the annual business decisions the insurance company has to make.
Modelling Expected Loss
Specifically, the most important aspect of this project is to correctly model the client loss. Otherwise known as the loss/cost model. There are several methods to model expected losses but the most ubiquitous approach is to model the frequency and severity of claims.
Frequency of Claims
The frequency of claims refers to the number of claims can occur for a particular client. We can denote this by $Y_f$.
To model $Y_f$ we should consider distributions that model count data. Those distributions include but are not limited to
Poisson
Negative Binomial Binomial
Zero-inflated Poisson
The most standard approach for modelling such data is through the use of GLM's which we modelled in class.
Severity of Claims
The Severity of claims refers to the monetary loss of an insurance claim. We denote this by $Y_s$.
To model $Y_s$ we should consider distributions that model continous data.
Gaussian (log-link)
Gamma (log-link)
Log-normal
Variance-Gamma
Generalized Hyperbolic
Again if we consider a GLM framework, we can easily use the data given in the project to model such losses.
Loss-Cost Model
To calculate the expected loss, use the following formula.
$$ ExpectedLoss = Y_s * Y_f $$
Essentially this is straight forward. You take the expectation of the number of claims for a particular client, and multiply by their severity (the expected monetary loss).
Evaluation
You will be evaluated in two phases.
Phase - 1
The first phase will be purely based on quantitative performance. You will develop your model and ship your premiums using the template potential_clients.csv. I will then take each of your premiums, and pit you up-against each other, to simulate a market. The lowest premium will have a 75% chance of acquiring the client. The rest of you will have a random chance to acquire the client via a uniform dirichlet process.
Phase - 2
Given that you have become bankrupt, you must re-evaluate your model performance, and submit a 6-page writeup detailing improvements and model developments. Once submitted, you will be evaluated again based on the merits of your improvements.