Actuarial Science: Modeling The objective of this report is to investigate dependence structure between the home line of business and domestic motor line of business to determine the global amount of capital to hold for both lines of business. The paper uses the regression analysis and descriptive statistics to analyze the raw data collected for the losses on both lines of business. The results from the analysis reveal that there is little or no positive dependence structure between the two lines of business because the R. Square value from the regression analysis output is 0.29, which is closer to 0. Moreover, there are higher losses in the domestic motor line of business than the home line of business. There is also higher volatility in the domestic motor line of business than home line of business. Thus, the report recommends that home line of business should attract more global capital than the domestic motor line of business.

Introduction

The objective of research is to use actuarial modeling and fit loss data into a gamma distribution to determine whether the dependence structure between the home line of business and domestic motor line of business is to be taking into account when determining the global amount of capital to hold for both lines. The paper establishes whether there is a positive dependence between home and domestic motor lines of business.

Assumption

Correlation between different lines of business in the United States is critical in assessing the aggregate of portfolio risks. Modeling is carried out using an analysis-synthesis paradigm. (Benfield, 2009).The analysis is carried out using the data on the losses on the domestic line of business and motor line of business using the regression analysis and descriptive statistics.

The assumption used to carry out the analysis between home line of business and domestic motor line of business is to use a linear relationship model with +1 indicating that a perfect linear relationship between home line of business and domestic motor line of business line. On the other hand, -1 indicates perfect decreasing relationships. The closer the coefficient to +1, the stronger...

The study uses R-Square to establish the statistical confidence.
Analysis of the Data

The study carries out the statistical analysis on the raw data on losses of home line of business and losses of the domestic motor line of business using the descriptive statistics. The descriptive statistics assists is summarizing the whole raw data in a manageable form. Using the descriptive statistics, the paper has been able to present the mean, standard deviation, median and variance of the whole data. The descriptive statistics also assists in comparing the home line of business with the domestic motor line of business and determine the global amount of capital to hold in those business lines.

Table 1: Descriptive Statistics

L1 (losses for Home line of business)

L2 ( losses for Domestic Motor line of business)

Mean

Standard Error

15.7346499

21.0997206

Median

2092.83193

Mode

#N/A

#N/A

Standard Deviation

Sample Variance

8895025.82

15995081.3

Kurstosis

5.6835354

5.99088783

Skewness

1.96918409

1.98859162

Range

31738.8805

42425.0881

Minimum

0.05521071

0.07189203

Maximum

31738.9357

42425.16

Sum

107843395

144406272

Count

35928

35928

Level of Statistical Confidence (95.0%)

30.8403853

41.3560846

The Mode is the most repeated value in the data. From the table 1, the mode is not available because there is no repeated value in the data of the home line of business and domestic motor line of business data set. (North Carolina State University, 2004). Thus, the paper uses the Mean value to compare the losses in the home line business to the domestic motor line of business. The Analysis reveals that the…