The linear model is named so because of the linear relationship between the input (independent variable) and the output (dependent variable). Even though we know it's of a high probability that the real-world data shows nonlinearity, people usually keep regarding the linear model as one of the top choices. The reasons for that are mainly two things. First, with acceptable approximation, the linear model is one of the simplest models to interpret. Second, the low complexity of the linear model makes it very unlikely to overfit the data, especially when you have small n (sample size) and large p ( variable number).

In order to obtain reasonably accurate full loss distributions via a nested simulations approach as described in Bauer et al. (2012), their cash-flow-projection (CFP) models would need to be simulated several hundred thousand times. But the insurers are currently far from being endowed with sufficient computational capacities to perform such expensive simulation tasks. By applying suitable approximation techniques like the least-squares Monte Carlo (LSMC) approach of Bauer & Ha (2015), the insurers are able to overcome these computational hurdles though. For example, they can implement the LSMC framework formalized by Krah et al. (2018) and applied by e.g. Bettels et al. (2014) to derive their full loss distributions. The central idea of this framework is to carry out a comparably small number of wisely chosen Monte Carlo simulations and to feed the simulation results into a supervised machine learning algorithm that translates the results into a proxy function of the insurer's loss (output) with respect to the underlying risk factors (input). To guarantee a certain approximation quality, the proxy function has to pass an additional validation procedure before it can finally be used for the full loss distribution forecast. Machine Learning Calibration Algorithm Apart from the calibration and validation steps, we adopt the LSMC framework from Krah et al. (2018) without any changes.