In this paper, we have used an algorithm to fit the Burr XII distribution to a set of insurance data. As it is well known, the probability of ultimate ruin is obtained as a solution to an integro-differential equation and in case, the claim severity is distributed as Burr XII distribution, this equation has to be solved numerically to obtain an approximation to the probability of ultimate ruin. Two numerical algorithms, namely the stable recursive algorithm and the method of product integration have been used to obtain numerically an approximation to this probability of ultimate ruin. The use of these two numerical algorithms provides a scope for comparing the consistency in values obtained by them. The first two moments of the time to ruin in case of Burr XII distributed claim severity have also been computed using the probability of ultimate ruin obtained through the stable recursive algorithm as an input. All these computations have been done under the assumption of the classical risk model.

In this paper, we have fitted two heavy tailed distributions viz the Weibull distribution and the Burr XII distribution to a set of Motor insurance claim data. As it is known, the probability of ruin is obtained as a solution to an integro differential equation, general solution of which leads to what is known as the Pollaczek-Khinchin Formula for the probability of ultimate ruin. In case, the claim severity is distributed as the above two mentioned distributions, and Pollaczek-Khinchin formula cannot be used to evaluate the probability of ruin through inversion of their Laplace transform since the Laplace Transforms themselves don't have closed form expression. However, an approximation to the probability of ultimate ruin in such cases can be obtained by the Pollaczek-Khinchin formula through simulation and one crucial step in this simulation is to simulate from the corresponding Equilibrium distribution of the claim severity distribution. The paper lays down methodologies to simulate from the Equilibrium distribution of Burr XII distribution and Weibull distribution and has used them to obtain an approximation to the probability of ultimate ruin through Pollaczek-Khinchin formula by Monte Carlo simulation. An attempt has also been made to obtain numerical values to the probability function for the number of claims until ruin in case of zero initial surplus under these claim severity distributions and this in turn necessitates the computation of the convolutions of these distributions. The paper makes a preliminary effort to address this issue. All the computations are done under the assumption of the Classical Risk Model.

The Weibull distribution due to its suitability to adequately model data with high degree of positive skewness which is a typical characteristics of the claim amounts, is considered a versatile model for loss modeling in general Insurance.In this paper, the Weibull distribution is fitted to a set of insurance claim data and the probability of ultimate ruin has been computed for Weibull distributed claim data using two methods, namely the Fast Fourier Transform and the 4 moment Gamma De Vylder approximation. The consistency has been found in the values obtained from the both the methods. For the same model, the first two moments of the time to ruin, deficit at the time of ruin and the surplus just prior to ruin have been computed numerically. The moments are found to be exhibiting behavior consistent to what is expected in practical scenario. The influence of the surplus process being subjected to the force of interest earnings and tax payments on the probability of ultimate ruin, causes the later to be higher than what is obtained in the absence of these factors.

The environmental concern of Medical Waste (MW) generation has escalated to an alarming level due to the versatility and high demand in various applications due to COVID 19. Reusing MW to make construction material looks to be an environmentally acceptable solution to finding an effective way to use them. This is also because traditional building materials take a lot of energy to manufacture, which has numerous negative environmental consequences. This paper summarises prior investigations on repurposing various MW as a construction raw material and aggregate, as well as their quality, with a focus on bricks and paving blocks. This research begins by demonstrating the characteristics of plastics and the environmental effects of MW. After that, there will be a talk of MW reuse and how it influences total construction material quality. According to this study, only a few investigations on the use of MW in the production of paving blocks have been conducted. Furthermore, the majority of studies used compressive strength and water absorption as the principal criteria for evaluating brick and paving block quality. The compressive strength is found to be 12-13 N/mm2 and water absorption is found to be less than 1% for the prepared sample.

The Probability of ultimate ruin under the classical risk model is obtained as a solution of an integro -differential equation involving convolutions and we have used Fast Fourier Transform (FFT) to obtain the approximate values of the probability of ultimate ruin from this integro -differential equation under the situation when the claim severity is modelled by the Mixture of 3 Exponentials and the Weibull distribution. Another application of FFT in ruin theory is shown by means of applying it to obtain the quantiles of the aggregate claim distribution under these claim severity distributions. Extension of the application of FFT is shown by using it to obtain the first moment of the time to ruin under the classical risk model for these distributions. The distributions which have been used are such that one is light tailed and the another is heavy tailed so that a comparison can be made between them on the precision of the actuarial quantities obtained through FFT. FFT has been found to be efficient in obtaining these actuarial quantities when used in conjunction with certain modifications like exponential tilting to control the aliasing error.