Monte Carlo Simulation

This powerful statistical simulation tool has a near-perfect application to the self funded health care plan. A sample Monte Carlo Simulation is attached. It models the plan and show these important items of information:

Purposes

What the expected claims would be if the plan were run without stop-loss of any kind. Such expected claims are ranged at 67%, 95% and 99.7% comfort levels.
What the expected claims would be if the plan were run with specific stop-loss only. Such expected claims are ranged at 67%, 95% and 99.7% comfort levels.
What the expected claims would be if the plan were run with both specific and aggregate stop-loss. The likelihood of an aggregate claim is shown.
The economic value of the specific and aggregate stop-loss and its comparison with gross stop-loss premiums is by product.
Of particular utility is the economic value of fine-timing stop-loss terms.

Requisite Data

Usually such simulation is a by-product (exhibit III) of the Annual Actuarial Report and requires no additional data.

Fees

When used as above, the fees are per simulation by this sliding scale.

· First three simulations $250

· Next three simulations 200

· Over six simulations 100

Work Product

See Attachment A.

ATTACHMENT A

MONTE CARLO SIMULATION – TRADITIONAL FORMAT

HEALTH CAR PLAN OF THE ABC COMPANY

A. BACKGROUND

Monte Carlo Simulation is a technique of sampling using millions of numbers stored randomly in a computer. A sample of l,000,e.g., would be represented by a series of l,000 of such numbers beginning with the nth number (seed of n, i. e.). Each such number represents a trial similar to the toss of a coin or the throw of a die. Such simulation becomes practical when the underlying probability curve is mathematically represented as with the well-known normal curve, e.g. The probability curve, which represents health care claims, is the lognormal curve; such is similar to the normal curve except the lognormal curve has an extremely long right-tail representative of rare but very large claims.

Actuarial Caveats. Simulation, modeling, sampling, etc., are, at best, an inexact science. The past is not necessarily the best judge of the future. The tragedy of the six-foot person drowning while crossing the river whose average depth measured five-feet must always be kept in mind. Simulation may reinforce, but not replace, common sense. Particularly challenging to the simulator are the numerous characteristics (economic, social, geographic, demographic, e.g.) which may vary by plan and plan year.

B. RELEVANT FACTS OR ASSUMPTIONS

1. Plan Year to which simulation applies is January 1, 1998 to January 1. 1999.

2. Medical plan enrollees assumed to be constant throughout the plan year

a. I 2,630; P/C 778; P/S 316; P + 1 ; F 355; Total 4,079

b. Number of covered persons is 6,499.

3. Projected paid claims for Plan Year

Benefit	Below Specific	Above Specific	Total
Medical	$10,950,000	$250,000	$11,200,000
Dental	1,250,000	0	1,250,000
Rx Card	2,000,000	0	2,000,000
Other		0	0
Total	$14,200,000	$250,000	$14,500,000

Specific is $150,000

4. 4. Aggregate benefit of $17,569,247 is allocated among:

Medical $13,545,000

Dental $1,546,000

Rx Card $2,478,347

Other _________

Total $17,569,247

5. Number of covered persons filing at least one medical claim 5,199.

6. Simulation based upon 100 trials is assumed to claim follow the lognormal frequency distribution. The lognormal is similar to the normal (bell-shaped) curve except the lognormal has a very right-handed tail.

7. In setting lognormal ,the mean is $2,779 the standard deviation is $10,282

seed number for Monte Carlo purposes is 3.

C. SIMULATION RESULTS

1. 1. Projected plan costs for the Plan Year shown above and set forth as set forth in the COBRA calculation, feasibility study or proposal are as follows:

	a. Actuarially-determined claims above the specific stop-loss attachment point.	$14,200,000
	b. Fixed Costs • Specific Stop-loss • Aggregate Stop-Loss • Administration	$580,135 29,498 979,292
	c. Reserve Maintenance	514,000
	Total	$16,302,925

Using Monte Carlo simulation, the projected total claims, without the purchase of stop-loss coverage are $14,148,891. Total actual claims will be in the ranges (confidence intervals) below indicted:

Confidence Percentage	Minimum	Maximum
50%	$14,089,629	$14,732,629
95%	13,768,129	15,054,129
99.7%	13,446,629	15,685,296

3. With the proposed stop-loss attachment point of $150,000 specific-only the expected total claims are $14,148,891 which means that the economic value of such aggregate stop-loss to the plan is $262,238. Total actual claims will be in the ranges (confidence intervals) below indicated:

Confidence Percentage	Minimum	Maximum
50%	$13,636,756	$14,661,026
95%	13,124,621	15,173,161
99.7%	12,612,486	15,685,296

With the proposed stop-loss attachment points of $150,000 specific and $17,569,247 aggregate, the expected total claims are $17,569,247 which means that the economic value of such aggregate stop-loss to the plan is $0. There is a 0% that the plan will have an aggregate claim for the Plan Year.

D. ACKNOWLEDGMENT

This simulation was prepared by Canton Harker, FSA, MAAA, principal of Self-Funding Actuarial Services, Inc., 8025 North Point Blvd., Suite 207 W. Winston-Salem, NC 27106 at the request of XYZ TPA.

514,000