Chapter 30: Reinsurance (2)

Question 1

Reasons for reinsuring: (5)

Answer 1

1. reducing parameter and claim payout fluctuations risks.
2. financing new business strain - use financial reinsurance and/or quota share
3. obtaining technical assistance
4. benefiting from regulatory or tax arbitrage opportunities
5. reducing costs.

Question 2

Parameter risk

Answer 2

There is a risk that the level of claims may be different from expected.

Question 3

Claim payout fluctuations - the variance relative to the mean can be high because: (2)

Answer 3

1. there are a small number of contracts for very high levels of cover
2. the lives insured are not independent risks.

Question 4

Reason for reinsuring - financing new business strain

Answer 4

A cedant can use reinsurance to reduce the financial risk associated with new business, either through an increase in its available capital or through a reduction in its financing requirement.

Question 5

Reason for reinsuring - Technical assistance

Answer 5

1. Reinsurance companies may have a considerable degree of expertise on such matters as:
   - underwriting,
   - product design,
   - pricing and
   - systems design.

Question 6

Reason for reinsuring - Cost reduction

Answer 6

Due to various reasons (including different capital requirements, diversification benefits, different taxation and different assessment of risks) a reinsurer may be able to price the risk at a lower cost than the cedant.

Question 7

Considerations before reinsuring (5)

Answer 7

1. cost of reinsurance
2. counterparty risks
3. legal risks
4. type of reinsurance
5. amount of reinsurance (choosing retention limits).

Question 8

Considerations before reinsuring - Cost of reinsurance

Answer 8

The reinsurer intends to make a profit as well as meet its cost of capital and expenses.

These costs will reduce the expected absolute level of profit for the cedant.

Question 9

Define: retention limit

Answer 9

The retention limit is the maximum amount of risk retained by the cedant on any individual risk.

Question 10

General factors to take into account when setting the retention limit: (9)

Answer 10

1. the average benefit level of the product and the expected distribution of the benefit.
2. the company’s insurance risk appetite
3. the level of the company’s free assets and the importance attached to stability of its free asset ratio
4. the terms on which reinsurance can be obtained and the dependence of such terms on the retention limit.
5. the level of familiarity of the company with underwriting the type of business involved
6. the effect on the company’s regulatory capital requirements of increasing or reducing the retention limit.
7. the existence of a profit-sharing arrangement in the reinsurance treaty
8. the company’s retention on its other products
9. the nature of any future increases in sums assured

Question 11

List approaches a cedant can use to determine the level at which the cedant should set its retention limit: (3)

Answer 11

1. Stochastic simulation - reinsurance only
2. Stochastic simulation - reinsurance with fluctuations reserve
3. Financial economics approach

Question 12

Stochastic simulation - reinsurance only (Retention limits) (3)

Answer 12

1. Set the retention limit at such a level as to keep the probability of insolvency (or ruin probability) below a specified level.
2. This can be done by using a stochastic model, so that claims can be projected forward together with the value of the company’s assets and liabilities.
3. By using a simulation, a retention level can then be determined such that the company stays solvent, or earnings stay above a certain level, for 995, say out of 1000 runs.

Question 13

Stochastic simulation - reinsurance with fluctuations reserve (Retention limits)

Answer 13

Consider the total of:

a) the cost of financing an appropriate mortality fluctuation reserve; and
b) the cost of obtaining reinsurance

As the retention limit increases, (a) will increase and (b) will decrease. A retention limit can then be adopted which minimises the total of (a) + (b).

Question 14

Financial economics approach (Retention limits)

Answer 14

Approach based based on the theory of efficient investment frontiers, and looks at reinsurance as an asset class that allows the firm to optimise its risk and reward trade off.

Question 15

Deposits back

Answer 15

• To manage counterparty risk in certain countries the supervisory authority may require the reinsurer to collateralise or “deposit back” its share of the total reserve under a reinsured contract with the cedant.

Question 16

The procedure for determining suitable retention limits (5)

Answer 16

1. Decide on some criterion for claim volatility beyond which the company cannot go. For example, you might want to have only 1% chance that the net loss from claims is at least 25m.
2. For differing retention limits model the function {total claims net of reinsurance} less {total premiums net of reinsured risk premiums}. This modelling will be done stochastically, varying the mortality experience.
3. The function is therefore: X = [C(g) - C(r)] - [P(g) - P(r)].
   The criterion would therefore be Pr(X > 25m) = 0.01.
4. Look at the results of this modelling and choose the retention limit that will satisfy your criterion.
5. We could use this as a retention limit (if the cover is available in the market at an acceptable price). However we could check if this could be done more cheaply using a mortality fluctuations reserve.

Question 17

The procedure for determining the optimal balance between a mortality fluctuation reserve and reinsurance: (5)

Answer 17

1. To do this we might assume that some of the cost of the risk premium reinsurance is instead going to be spent on financing a mortality fluctuation reserve. (The cost = M(j-i).
2. If we decide to redirect a proportion (w) of the reinsurance risk premium to the mortality fluctuations reserve, the the amount of mortality reserve purchased is: M = w * P(r) / (j - i), and (1-w) * P(r) left to buy reinsurance.
3. Now model the distribution of X under this new arrangement not that we now have a higher retention level: X = [C(g) - C’(r)] - [P(g) - P(r)] - M
4. Compare the protection offered under this new construction against that offered by the previous arrangement, i.e. recalculate Pr(X > 25m).
5. Try this for other levels of reinsurance / mortality fluctuations reserve. Then decide on which combination offers the most protection for a given cost.