Answered: Comparison of distribution tails).…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Please solve with the step max in 60-90 minutes the chapter actuarial

Comparison of distribution tails). Consider the distribution of losses owned by insurance companies. Loss for the coming year is predicted to have a mean of 100 with a standard deviation of 223.607.

If it is assumed that the loss distribution is Normal, Pareto and Gamma (with mean and variance above), determine VaR for each loss distribution with a safety level of 90%; 99% and 99.9%.

Notes:

From the mean and standard deviation as well as the k-th moment, the parameter values for each distribution (in millions) will be obtained. Furthermore, by using the inverse FDK, the VaR value will be obtained.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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