An Investigation of Machine Learning Approaches in the Solvency II Valuation Framework

Castellani, Gilberto; Fiore, Ugo; Marino, Zelda; Passalacqua, L.; Perla, Francesca; Scognamiglio, Salvatore; Zanetti, Paolo

doi:10.2139/ssrn.3303296

Cited by 14 publications

(16 citation statements)

References 17 publications

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“…Conceivable alternatives to the entire adaptive algorithm are other typical machine learning techniques such as artificial neural networks (ANNs), decision tree learning or support vector machines. In particular, the classical feed forward networks proposed by Hejazi and Jackson (2017) and applied in various ways by Kopczyk (2018), Castellani et al (2018), Born (2018) and Schelthoff (2019) were shown to capture the complex nature of CFP models well. A major challenge here is not only to find reliable hyperparameters such as the numbers of hidden layers and nodes in the network, batch size, weight initializer probability distribution, learning rate or activation functions but also the high dependence on the random seeds.…”

Section: Introductionmentioning

confidence: 99%

“…The gradient boosting machines, requiring more parameter tuning and thus being more versatile and demanding, came overall very close to the adaptive approaches. Castellani et al (2018) compared support vector regression (SVR) by Drucker et al (1997) to ANNs and the adaptive approaches by Teuguia et al (2014) in a seven risk factor example and found the performance of SVR placed somewhere inbetween the other two approaches with the ANNs getting closest to the nested simulations benchmark. As some further non-parametric approaches, Sell (2019) tested least-squares support-vector machines (LS-SVM) by Suykens and Vandewalle (1999) and shrunk additive least-squares approximations (SALSA) by Kandasamy and Yu (2016) in comparison to ANNs and the adaptive approaches by Krah et al (2018) with OLS regression.…”

Section: Introductionmentioning

confidence: 99%

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

Krah

Nikolić

Korn

2020

Risks

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Krah

Nikolić

Korn

2020

Risks

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“…In addition, we try different regularization techniques and test the adequacy of the neural network approximations using the defining property of the conditional expectation. Neural networks have also been used for the calculation of solvency capital requirements by Hejazi and Jackson (2017), Fiore et al (2018) and Castellani et al (2019). But they all exclusively focus on value-at-risk, do not make use of importance sampling and apply neural networks in a slightly different way.…”

Section: Introductionmentioning

confidence: 99%

Assessing Asset-Liability Risk with Neural Networks

Cheridito

Ery

Wüthrich

2020

Risks

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We introduce a neural network approach for assessing the risk of a portfolio of assets and liabilities over a given time period. This requires a conditional valuation of the portfolio given the state of the world at a later time, a problem that is particularly challenging if the portfolio contains structured products or complex insurance contracts which do not admit closed form valuation formulas. We illustrate the method on different examples from banking and insurance. We focus on value-at-risk and expected shortfall, but the approach also works for other risk measures.

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“…(2016) and Castellani et al . (2018). The former presents a regress-later model based on an orthogonal basis of piece-wise linear functions, and the latter a regress-now model based on neural networks.…”

Section: Introductionmentioning

confidence: 99%

A neural network model for solvency calculations in life insurance

Fernandez-Arjona

2020

Ann. actuar. sci.

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Insurance companies make extensive use of Monte Carlo simulations in their capital and solvency models. To overcome the computational problems associated with Monte Carlo simulations, most large life insurance companies use proxy models such as replicating portfolios (RPs). In this paper, we present an example based on a variable annuity guarantee, showing the main challenges faced by practitioners in the construction of RPs: the feature engineering step and subsequent basis function selection problem. We describe how neural networks can be used as a proxy model and how to apply risk-neutral pricing on a neural network to integrate such a model into a market risk framework. The proposed model naturally solves the feature engineering and feature selection problems of RPs.

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An Investigation of Machine Learning Approaches in the Solvency II Valuation Framework

Cited by 14 publications

References 17 publications

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

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

Assessing Asset-Liability Risk with Neural Networks

A neural network model for solvency calculations in life insurance

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