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.

Theoretical Analysis of Dynamic Behaviors in Liquid Chromatography

Theoretical Analysis of Dynamic Behaviors in Liquid Chromatography The chromatographic techniques are used on laboratory and industrial scales for the sepa- ration of substances that under the traditional processes, such as distillation or extraction, are neither technically nor economically feasible. It is an important separation technique in the petrochemical industry and becomes more and more exploited in fine chemical, phar- maceutical and biotechnical industries. For instance, this attractive technology is used to separate chiral molecules, enzymes, sugar and to purify proteins or to produce insulin. This thesis project is concerned with the analytical and numerical solutions of three stan- dard liquid chromatographic models namely, the equilibrium dispersive model (EDM), the lumped kinetic model (LKM) and the general rate model (GRM). Each model consid- ers different levels of complexities to describe the process. These models are systems of convection-diffusion partial differential equations with dominating convective terms and coupled through differential or algebraic equations. The Laplace transformation is applied to derive the analytical solutions of the EDM and LKM considering the special case of single-component linear adsorption isotherm, contin- uous or finite width pulse injections, two different sets of boundary conditions and fully porous particles. For further analysis of the solute transport behavior, the analytical tem- poral moments are derived from the Laplace-transformed solutions and are compared with the numerical solutions of a semi-discrete high resolution finite volume scheme (HR-FVS). For nonlinear adsorption isotherms, numerical techniques are the only tools to provide solu- tions. However, the strong nonlinearities of realistic thermodynamic functions pose major difficulties for the numerical schemes. For that reason, computational efficiency and accu- racy of the numerical methods are highly important. The suggested HR-FVS is extended to approximate these nonlinear model equations. The numerical results of the suggested HR-FVS are compared with some other finite volume schemes available in the literature. Different case studies are considered covering a wide range of mass transfer kinetics. The results obtained verified the correctness of analytical results and accuracy of the suggested HR-FVS. An interesting aspect of this thesis project is the application of GRM to fixed-bed chro- matographic columns packed with core-shell or fully porous particles. Due to their proven performance and improved availability, core-shell particles are increasingly applied for chro- matographic separations. Such particles are useful for highly efficient and fast separation of complex samples with a reasonably low back pressure. Cored beads provide advantages over fully porous beads, such as reduced diffusional mass transfer resistances in particle macropores and separation times. The concept has improved column efficiency by shorten- ing the diffusion path that molecules have to travel and thus, has improved the diffusional mass transfer kinetics in particle macropores. Once again, both single-component linear and multi-component nonlinear GRM models are considered. The above mentioned ana- lytical and numerical solution techniques are applied to solve the model equations. The potential of the solutions is demonstrated by considering different case studies that quan- tify the effects of the relative core size, axial dispersion, film mass transfer resistance and intraparticle diffusion resistance in the porous layer on the elution curves.