Implementation of Gaussian Process Regression in Estimating Motor Vehicle Insurance Claims Reserves

This study aims to calculate the allowance for losses by applying Gaussian Process regression to estimate future claims. Modeling is done on motor vehicle insurance data. The data used in this study are historical data on PT XYZ's motor vehicle insurance business line during 2017 and 2019 (January 2017 to December 2019). Data analysis will be carried out on the 2017 - 2019 data to obtain an estimate of the claim reserves in the following year, namely 2018 - 2020. This study uses the Chain Ladder method which is the most popular loss reserving method in theory and practice. The estimation results show that the Gaussian Process Regression method is very flexible and can be applied without much adjustment. These results were also compared with the Chain Ladder method. Estimated claim reserves for PT XYZ's motor vehicle business line using the chain-ladder method, the company must provide funds for 2017 of 8,997,979,222 IDR in 2018 16,194,503,605 IDR in 2019 amounting to Rp. 1,719,764,520 for backup. Meanwhile, by using the Bayessian Gaussian Process method, the company must provide funds for 2017 of 9,060,965,077 IDR in 2018 amounting to 16,307,865,130 IDR, and in 2019 1,731,802,871 IDR for backup. The more conservative Bayessian Gaussian Process method. Motor vehicle insurance data has a short development time (claims occur) so that it is included in the short-tail type of business.

Nanofluid Flows in Different Geometries

Many conventional fluids, such as water, sodium alginate, organic liquids (e.g., propylene and ethylene glycols, etc.) and some others, are quite often used in various engineering and industrial processes as coolants. The use of water in car radiators is a very basic example. Nowadays, scientists are keenly looking for ways to enhance the performance of engines and such equipment where these coolants are being used. Conventionally, the heat transfer capability of these liquids is not up to the mark. Therefore several attempts have been made to enhance their thermo-physical capabilities. The use of nanofluids is one of such efforts. Scientists, over the past few decades, have been working on the idea of mono-nanofluids (nanofluids with single nanomaterials), to enhance the thermal efficiency of these traditional fluids. However, to improve the number of desirable features of mononanofluids, a novel subject of hybrid nanofluids (nanofluids with two or more nanomaterials) has come into existence. It exhibits superior thermo-mechanical properties when compared to mono nanofluids. In this manuscript, a number of thermal conductivity models, for both mono and hybrid nanofluids, have been employed to see the working of these models in different geometries. In the case of hybrid nanofluids, the modified versions of the models (such as Renovated Hamilton and Crosser’s model, Bruggeman’s model, Hamilton and Crosser’s model, Maxwell’s model, and Xue’s model) for thermal conductivity have been considered. The flow of mono as well as hybrid nanofluids inside an expanding\contracting domains, rectangular conduit with the lower stretchable wall, curved stretching surface, and curved channels, have been studied in details. A novel analysis of hybrid nanofluid flow between two Riga plates is also a part of this manuscript. Moreover, the squeezing flow of a hybrid nanofluid inside a rotating rectangular conduit, with lower stretchable walls, has also been investigated. The impact of the externally applied magnetic field, along with the internal heat generation phenomena, on the flows and heat transport mechanism of some mono and hybrid nanofluids have thoroughly been examined. Heat and mass transfer under the influence of nonlinear thermal radiation and chemical reaction effects in several geometries have been studied in this manuscript. xi In our analysis, we have used certain similarity transformations and scaling parameters to reduce the governing partial differential equations to the corresponding systems of nonlinear ordinary differential equations (dimensionless). This process reduces the number of variables, and parameters, which leads to a relatively more straightforward mathematical treatment. However, the resulting systems are still complicated enough to have an exact solution. For their treatment, we have discussed the implementation of several approximation techniques based on the method of weighted residuals and wavelet methods. We have also proposed some modifications in wavelet methods for a better and more flexible implementation. The plots for velocity, together with temperature, and concentration profiles (wherever applicable) are presented to capture the effects of involved parameters on the respective profiles. It has been found that the addition of nanomaterials significantly boosts the thermal and heat transport properties of the host fluid and that these phenomena are more prominent for the hybrid nanofluids.