# Insurer Ruin

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In insurer insolvency proceedings, it is typical for the claims of insureds to have a higher priority against the assets of the insurer than the claims of ordinary debt creditors or equity holders. To reduce the risk that insured claims or investor claims will go unpaid by an insurer experiencing financial difficulties or a bad year or two, regulators and rating agencies often require the insurer to have significant assets available to pay insureds' claims. This Demonstration explores how laws relating to the capitalization required of an insurer couple with a variety of other parameters involving the limits of the insurance policy, the revenue received by the insurer, the expenses of the insurer, and the rates available in the capital market to determine the financial success of the insurer over a user-specified period of simulation. It is intended to show, among other things, the size of the premium the insurer must charge to avoid "ruin", in which the costs of recapitalization needed to meet regulatory requirements become a crippling burden.

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Contributed by: Seth J. Chandler (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

There are six sets of parameters. Five sets are on the leftÃ¢Â€Âhand side of the display. Many of the parameters are ratios of some quantity to "mean net payments", the amount the insurer pays on average to insureds over the period of the simulation.

1. The first set relates to the layer of insurance coverage provided by the insurer. You determine the "attachment point". An attachment point of 0.5 means that the insurer pays nothing until the losses of an insured exceed 0.5. You determine the "layer size" or "policy limit". A layer size of 1.5 means that the most an insurer will pay is 1.5. Thus a policy with an attachment point of 0.5 and a layer size of 1.5 (often denoted "1.5 XS 0.5") pays 1.2 on a loss of 1.7.

2. You set parameters related to the revenue received by the insurer. You set a ratio between the annual premiums received by the insurer and mean net payments. Often this will be greater than 1 to take account of various expenses faced by the insurer and to provide a cushion against bad years. You also set an initial level of capitalization, again relative to the mean net payments.

3. You set two parameters relating to the expenses incurred by the insurer. You set a "premium load" coefficient that is multiplied by premiums received to approximate the costs of writing policies. You set a "payment load" coefficient that is multiplied by the amount paid by the insurer to approximate the cost of adjusting claims.

4. You set parameters related to the capital market. These are the return the insurer makes on its investments, the amount it must pay to borrow in order to recapitalize, and the return it pays investors on its surplus (equity).

5. You set a regulatory parameter related to the amount of assets relative to mean net claims regulators or rating agencies require the insurer to have. A value of 4 means that regulators or rating agencies effectively require the insurer to maintain in assets first available to pay insured claims an amount equal to four times the expected amount of claims each year (not including various loadings).

6. On the right side you set parameters relating to the distribution of losses suffered by the insured. You choose the family of distributions from which the losses are generated. Hovering your mouse over the associated buttons lets you see the cumulative density function of the parameterized version of the distribution you chose. You set the parameters of the distribution from which the random losses are generated. You set how many insureds will be in the insurance pool. And you set how many years the simulation will examine.

Assets each year are equal to the sum of (1) the prior assets plus the return on investments; (2) the premium; and (3) any borrowings needed to satisfy the regulatory constraint less the sum of (a) the return on equity; (b) interest payments on borrowings (if any); (c) the premium load; (d) claims paid; and (e) claims load. Surplus is equal to assets less borrowings.

Notice that once the insurer's surplus plunges below the regulatory constraint, it becomes ever more difficult for the insurer to maintain a positive surplus. This is so because the insurer has to borrow generally at high rates in order to meet regulatory requirements. The interest rates on these loans can become a crushing burden on the insurer.

Users may wish to explore the premiums and initial capitalization needed for various other parameters to keep the insurer largely or exclusively "out of the red" for the duration of the simulation. Examine, for example, how changing the number of insureds in the pool alters the premium needed. Or examine how changes in the interest rate for borrowing affect the needed premium. One can also consider how changes in the distribution from which losses are generated affect needed initial capitalization levels and annual premiums.

Snapshot 1: viewing the output in statistics mode

Snapshot 2: a time series for a larger layer and a lower premium ratio

Snapshot 3: a higher regulatory constraint and a higher premium ratio

Snapshot 4: a time series of payments, operating profit, and change in surplus

Snapshot 5: a time series for a lower premium

## Permanent Citation

"Insurer Ruin"

http://demonstrations.wolfram.com/InsurerRuin/

Wolfram Demonstrations Project

Published: March 7 2011