Inside the Solvency 2 Black Box: Net Asset Values and Solvency Capital Requirements with a Least-Squares Monte-Carlo Approach

2014 ◽  
Author(s):  
Anthony Floryszczak ◽  
Olivier Le Courtois ◽  
Mohamed Majri
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
Capital Requirements ◽  
Black Box ◽  
Monte Carlo Approach ◽  
Least Squares Monte Carlo ◽  
Asset Values ◽  
Solvency Capital

scholarly journals Least-Squares Monte Carlo for Proxy Modeling in Life Insurance: Neural Networks

Risks ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 116
Author(s):  
Anne-Sophie Krah ◽  
Zoran Nikolić ◽  
Ralf Korn
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Monte Carlo ◽  
Least Squares ◽  
Capital Requirements ◽  
Sensitivity Analyses ◽  
Approximation Technique ◽  
Data Set ◽  
Least Squares Monte Carlo ◽  
Feed Forward Neural Networks

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.

scholarly journals Testing the Least-Squares Monte Carlo Method for the Evaluation of Capital Requirements in Life Insurance

Risks ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 48
Author(s):  
Massimo Costabile ◽  
Fabio Viviano
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Least Squares ◽  
Closed Form ◽  
Life Insurance ◽  
Numerical Experiments ◽  
Capital Requirements ◽  
Basis Functions ◽  
Evaluation Framework ◽  
Least Squares Monte Carlo

In this paper, we test the efficiency of least-squares Monte Carlo method to estimate capital requirements in life insurance. We choose a simplified Gaussian evaluation framework where closed-form formulas are available and allow us to obtain solid benchmarks. Extensive numerical experiments were conducted by considering different combinations of simulation runs and basis functions, and the corresponding results are illustrated.

scholarly journals Machine Learning in Least-Squares Monte Carlo Proxy Modeling of Life Insurance Companies

Risks ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 21 ◽  
Author(s):  
Anne-Sophie Krah ◽  
Zoran Nikolić ◽  
Ralf Korn
Keyword(s):  
Machine Learning ◽  
Monte Carlo ◽  
Least Squares ◽  
Life Insurance ◽  
Capital Requirements ◽  
Multivariate Adaptive Regression Splines ◽  
Insurance Companies ◽  
Least Squares Regression ◽  
Least Squares Monte Carlo ◽  
Proxy Modeling

Under the Solvency II regime, life insurance companies are asked to derive their solvency capital requirements from the full loss distributions over the coming year. Since the industry is currently far from being endowed with sufficient computational capacities to fully simulate these distributions, the insurers have to rely on suitable approximation techniques such as the least-squares Monte Carlo (LSMC) method. The key idea of LSMC is to run only a few wisely selected simulations and to process their output further to obtain a risk-dependent proxy function of the loss. In this paper, we present and analyze various adaptive machine learning approaches that can take over the proxy modeling task. The studied approaches range from ordinary and generalized least-squares regression variants over generalized linear model (GLM) and generalized additive model (GAM) methods to multivariate adaptive regression splines (MARS) and kernel regression routines. We justify the combinability of their regression ingredients in a theoretical discourse. Further, we illustrate the approaches in slightly disguised real-world experiments and perform comprehensive out-of-sample tests.

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