Abstract
The least-squares Monte Carlo method has proved to be a suitable approximation technique for the calculation of a life insurer’s solvency capital requirements. We suggest to enhance it by the use of a neural network based approach to construct the proxy function that models the insurer’s loss with respect to the risk factors the insurance business is exposed to. After giving a mathematical introduction to feed forward neural networks and describing the involved hyperparameters, we apply this popular form of neural networks to a slightly disguised data set from a German life insurer. Thereby, we demonstrate all practical aspects, such as the hyperparameter choice, to obtain our candidate neural networks by bruteforce, the calibration (“training”) and validation (“testing”) of the neural networks and judging their approximation performance. Compared to adaptive OLS, GLM, GAM and FGLS regression approaches, an ensemble built of the 10 best derived neural networks shows an excellent performance. Through a comparison with the results obtained by every single neural network, we point out the significance of the ensemble-based approach. Lastly, we comment on the interpretability of neural networks compared to polynomials for sensitivity analyses.
Highlights
Solvency Risk CapitalUnder Solvency II regulation, insurance companies are required to determine a full probability distribution forecast of the changes in their available capital (AC) over a one-year period.Solvency Capital Requirement (SCR) represents the change in AC which is exceeded in only 0.5% of all one-year scenarios
While the scenarios are the realizations of the explanatory variables in the regression or training, the values denote the realizations of the response variable, such as the AC or best estimate liability (BEL), which we aim to find a proxy function for
In the third in our series of articles, we have moved beyond linear models in our attempts to build proxy functions for insurance risk capital calculations
Summary
Under Solvency II regulation, insurance companies are required to determine a full probability distribution forecast of the changes in their available capital (AC) over a one-year period. Solvency Capital Requirement (SCR) represents the change in AC (usually a loss) which is exceeded in only 0.5% of all one-year scenarios. For life insurers Solvency II regulation poses an enormous computational challenge, since they need to compute the change in AC in a large number of one-year scenarios, but for each of these scenarios they have to perform a stochastic valuation of the future cash flows. Formula which allows them to estimate SCR without deriving the probability distribution forecast, it usually uses a proxy function for the stochastic valuation of the future cash flows. A large saving potential can be realized if the proxies become more efficient and accurate
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