Non-life insurance pricing is the art of setting the price of an insurance policy, taking into consideration varoius properties of the insured object and the policy holder. Introduced by British actuaries generalized linear models (GLMs) have become today a the standard aproach for tariff analysis.
These notes aim at giving a broad skill set to the actuarial profession in insurance pricing and data science. We start from the classical world of generalized linear models, generalized additive models and credibility theory. These methods form the basis of the deeper statistical understanding. We then present several machine learning techniques such as regression trees, bagging, random forest, boosting machines and neural networks. Finally, we provide methodologies for analysing telematics car driving data from unsupervised learning.
Non-life Insurance Pricing With Generalized Linear Models Pdf Download
Keywords: non-life insurance pricing, car insurance pricing, generalized linear models, generalized additive models, credibility theory, neural networks, regression trees, CART, bootstrap, bagging, random forest, boosting, telematic data, data science, machine learning, data analytics
The classes SGDClassifier and SGDRegressor providefunctionality to fit linear models for classification and regressionusing different (convex) loss functions and different penalties.E.g., with loss="log", SGDClassifierfits a logistic regression model,while with loss="hinge" it fits a linear support vector machine (SVM).
One common pattern within machine learning is to use linear models trainedon nonlinear functions of the data. This approach maintains the generallyfast performance of linear methods, while allowing them to fit a much widerrange of data.
We see that the resulting polynomial regression is in the same class oflinear models we considered above (i.e. the model is linear in \(w\))and can be solved by the same techniques. By considering linear fits withina higher-dimensional space built with these basis functions, the model has theflexibility to fit a much broader range of data.
Skewed data is the main issue in statistical models in healthcare costs. Data transformation is a conventional method to decrease skewness, but there are some disadvantages. Some recent studies have employed generalized linear models (GLMs) and Cox proportional hazard regression as alternative estimators.
Statistical models are often used in many healthcare economics and policy studies. The main issues in such studies are the estimation of mean population healthcare costs and finding the best relationship between costs and covariates through regression modeling [1]. However, these cannot be implemented by simple statistical models as the healthcare costs data have specific characterizations [2]. Healthcare costs data demonstrate the substantial positive skewness and are sometimes characterized by the use of large resources with zero cost [3]. These specifications of data impose a number of difficulties in using standard statistical analysis, such as implementing linear regression causes unreliable results [2].
Two-part models based on mixture models are performed when excess zeroes are present in data [3]. Further, logarithmic (or other) transformations are commonly used to decrease the skewness and drive them close to normal distribution, in order to implement linear regression models. The logarithmic transformation with ordinary least squares (OLS) regression is a very common approach in applied economics. However, it also presents several drawbacks. One of these drawbacks is that the predictions are not robust enough to detect the heteroscedasticity in the transformed scale [1,4]. The general consensus is that estimating the mean cost using a logarithmic regression model leads to biased estimation [2,4-6].
An alternative approach is using nonlinear regression models, of which exponential conditional mean (ECM) models in generalized linear models (GLMs) are examples [7]. Generally, GLMs extend the linear modeling framework to allow response variables that are not normally distributed. In healthcare studies, generalized linear modeling through log-link function avoids the weakness and problems of OLS regression. In addition, the Cox proportional hazards model has been a controversial issue for healthcare data modeling. It has been used as a special flexible model for skewed healthcare data in many studies [8,9].
In P&C insurance, the challenge is to be strong in pricing sophistication in order to stay competitive. Proven and established actuarial models need to be combined with modern machine learning models to exploit the power of big data. 2ff7e9595c