Delong, Ł., Lindholm, M., Wüthrich, M.V., 2020, Fitting Gamma Mixture Density Networks with Expectation-Maximization algorithm
Working Paper,
05-10-2020
We discuss how mixtures of Gamma distributions with shape and rate parameters depending on explanatory variables can be fitted with neural networks. We develop two versions of the EM algorithm for fitting Gamma Mixture Density Networks which we call the EM network boosting algorithm and the EM forward network algorithm. The key difference between the EM algorithms is how we pass the information about the trained neural networks and the predicted parameters between the iterations of the EM algorithm. We validate our EM algorithms and test different methods of how the algorithms can be efficiently applied in practice. Our algorithms work for general mixtures of any distribution types that have closed form densities.
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Delong, Ł., Wüthrich, M.V., 2020, Neural networks for the joint development of individual payments and claim incurred
Published Paper,
27-02-2020
The goal of this paper is to develop regression models and postulate distributions which can be used in practice to describe the joint development process of individual claim payments and claim incurred. We apply neural networks to estimate our regression models. As regressors we use the whole claim history of incremental payments and claim incurred, as well as any relevant feature information which is available to describe individual claims and their development characteristics. Our models are calibrated and tested on a real data set, and the results are benchmarked with the Chain-Ladder method. Our analysis focuses on the development of the so-called Reported But Not Settled (RBNS) claims.
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Delong, Ł., 2013, Backward Stochastic Differential Equations with Jumps and their Actuarial and Financial Applications
Book,
10-04-2013
Backward Stochastic Differential Equations with jumps can be used to solve problems in both finance and insurance.
This book will make BSDEs more accessible to those who are interested in applying these equations to actuarial and financial problems. It will be beneficial to students and researchers in mathematical finance, risk measures, portfolio optimization as well as actuarial practitioners.
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