Insurance

Risk Management Examples

Chapter 7: Risk Analysis of Insurance Claims & Reinsure

In Book 13: Financial Risk Assessment and Management with Six Sigma DMAIC Methods

ISBN: 978-620-5-49700-5

Author: Vojo Bubevski

Abstract

This chapter presents a stochastic model for Insurance to analyse the possibility of being reinsured. Without reinsurance, the company pays all claims, net of deductibles, for its policyholders. With reinsurance, it pays a fixed premium to another insurance company, the reinsurer. There is a reinsurance deductible. If the company’s liability for all claims, again net of deductibles, is less than this deductible, the company is liable for all of it. However, if this liability is greater than the reinsurance deductible, the company is liable only for the deductible; the reinsurer pays the rest. Keywords: Risk Analysis, Insurance & Reinsurance, Claims, Insurance & Reinsurance Risk, What-If Analysis; Sensitivity Analysis; Monte Carlo simulation; Stochastic model.

The Results

The simulation resolved the Profit Insure distribution providing the results. 
The Mean is $443,213.51 M with a Standard Deviation of $88,097.77 M, i.e., 19.977%, which is an acceptable middle-low risk. The Six Sigma target parameters are TV = $442,510.00 M; LSL = $309,757.00 M; and USL = $508,886.50 M. The Six Sigma process capability metrics are Cp = 0.3767; Cpk = 0.2485; and σ-L = 0.2845. There is a 5.0% probability that the Mean will be below $306,000 M; a 90.0% probability that it will be in the range of $306,000 M – $532,000 M; and a 5.0% probability that it will be above $532,000 M.

Sensitivity analysis provides for identifying and quantifying the main contributors to variability and risk based on probability distribution. The analysis resolved the Profit Insure Inputs Ranked by Effect on Output Mean. The Inputs Ranked by Effect on Output Mean graph provided the following output. The analysis illustrated that the effect of the top variable, Total Claim Liability, on the Profit Insure Mean is a change in the range of $261,768.76 M to $534,234.48 M, which are respectively left and right from the Baseline of $443,213.51 M, which is marked on the graph. Other variables are less influential as their associated effects have smaller ranges.

 
Chapter 8: Insurance Claims Payments Risk Analysis
InBook 13: Financial Risk Assessment and Management with Six Sigama DMAIC Methods 

ISBN: 978-620-5-49700-5

Author: Vojo Bubevski
Abstract 

This chapter presents a risk analysis of insurance claims payments. The chapter explains how to model the uncertainty involved in the payment of insurance claims.  The model must account for the uncertainty in both the total number of claims and the dollar amounts of each claim made. A specific probability distribution is applied to determine the total number of claims.  Another specific probability distribution is used to determine the payment amount for each claim.  Also, the model calculates the total payment amount.

Keywords: Risk Analysis, Insurance, Claims Payments, Insurance Risk, What-If Analysis; Sensitivity Analysis; Monte Carlo Simulation; Stochastic model.

The Results

The Claim Pay Amount of results is presented in Table 1.

Table 1: Claim Pay Amount ($M)

Claim #

1

2

3

4

5

Pay Amount

120

140

160

180

200

Claim #

6

7

8

9

10

Pay Amount

220

240

260

280

300

Claim #

11

12

13

14

15

Pay Amount

320

340

360

380

400

Claim #

16

17

18

19

20

Pay Amount

420

440

460

480

500

Claim #

21

22

23

24

25

Pay Amount

520

540

560

580

600

Claim #

26

27

28

29

30

Pay Amount

620

640

660

680

700

Claim #

31

32

33

34

35

Pay Amount

720

740

760

780

800

Claim #

36

37

38

39

40

Pay Amount

820

840

860

880

900

Pay Amount starts with $120 M for Claim 1 and then increases with increments of $20 M, i.e., $120 M, $140 M, …, and $900 M, reaching $900 M for Claim 40.

The graph of the calculated Claim Pay Amount, for Claims from 1 to 40 presented the visual value labels given in dollars ($M).