Actuarial Analysis

Actuarial Analysis for Pricing, Reserving and Projecting Health Insurance Costs

Actuarial analysis turns the uncertain healthcare costs of individuals into an expected cost for a defined group and period, so that an insurer, sickness fund or government can set contributions, hold money back for claims and judge whether a scheme can pay its way. In health economics it lies behind premiums, the costing of benefit packages and official estimates of what a coverage change will cost, and it draws on the same inputs as economic evaluation, namely rates of service use, unit costs and the size of the covered population. Here the term refers to actuarial work on health insurance and health financing; the life-table survival technique called the actuarial method is a separate topic.

Expected claims cost as the building block

Pricing in health insurance starts from the expected cost of claims for one covered person over one period. For a single person that cost is highly uncertain, but the average across a large group is far more predictable, which is what makes insurance workable. The quantity of interest is an expected value, usually assembled service by service as follows.

$$\bar{C} = \sum_{i=1}^{k} f_i \, u_i$$

where $\bar{C}$ is the expected claims cost per covered person per year, $k$ is the number of benefit categories (inpatient days, outpatient visits, prescriptions and so on), $f_i$ is the utilisation rate of category $i$ in units per person per year and $u_i$ is its unit cost. Multiplying by the number of covered persons gives total expected spending, which is the approach the International Labour Office compendium on health care finance describes for projecting scheme expenditure.

Because use of care varies with age and sex, claims cost is normally estimated for separate rating groups, each large enough for its average to be reliable. That requirement follows from the arithmetic of risk pooling. With independent costs, the standard deviation of the average cost across $N$ people is given below.

$$SD(\bar{C}_N) = \frac{\sigma}{\sqrt{N}}$$

where $SD(\bar{C}_N)$ is the standard deviation of the average cost per person in a pool of $N$ people and $\sigma$ is the standard deviation of one person's annual cost. Real costs are not fully independent, since price rises and new treatments affect everyone at once, so this formula gives a lower bound on the uncertainty a scheme faces.

From expected claims to a premium or contribution rate

A premium has to cover more than expected claims. The ILO compendium separates the net or risk premium, which covers the expected cost of benefits, from the gross premium, which adds a supplement for administrative costs and a security margin for fluctuations. With a fixed and a proportional supplement, the annual gross premium is as follows.

$$G = \frac{P + \beta}{1 - \gamma}$$

where $G$ is the gross premium per covered person, $P$ is the net premium (expected claims cost per person), $\beta$ is a fixed loading per person, and $\gamma$ is the proportional loading, the share of gross premium set aside for variable expenses, margin and any profit. The loading is in effect the price of protection, the amount a member pays above expected claims for having the risk carried by the pool. The medical loss ratio used by some regulators looks at the same split from the other side.

Social health insurance applies the same logic to a contribution rate. Under pay-as-you-go financing the ILO compendium describes a scheme as in actuarial balance in a year when total contributions at least equal benefit spending plus operating expenses. The rate is set for the whole insured population rather than for rating groups, which is how social health insurance redistributes from low-risk to high-risk members. The link to welfare economics comes through Arrow, who showed that when insurers sell any policy at a premium depending only on its actuarial value (its expected payout), a risk-averse buyer chooses full cover above a deductible.

Reserves for claims not yet paid

Health claims are paid with a delay, so at any reporting date a scheme owes money for care already given. The US Actuarial Standards Board's Actuarial Standard of Practice No. 5, Incurred Health and Disability Claims, defines the unpaid claims liability as the unpaid portion of incurred claims, including unreported claims and claims reported but unpaid. One technique it names is the development or lag method, which groups past claims by the period in which they were incurred and the period in which they were paid, commonly by month, to build a payment pattern, as shown below.

$$\hat{I}_m = \frac{P_m}{c_d}$$

where $\hat{I}_m$ is the estimated total incurred claims for service month $m$, $P_m$ is the amount paid so far for that month, and $c_d$ is the completion factor, the cumulative share of a month's eventual claims that experience shows to have been paid by the end of $d$ months after the month of service. If 80% is usually paid within two months, £4 million paid for a month after two months implies about £5 million incurred.

This matters to anyone costing care from claims data. The latest months in an extract are incomplete, so unadjusted totals understate cost and suggest a spurious fall in spending. Separately, the ILO compendium notes that an actuary may recommend a contingency reserve of one or two months of expected benefit and administrative spending for a social health insurance fund.

Risk adjustment and the actuarial value of a plan

Where insurers compete but premiums cannot vary with expected cost, as under community rating or similar premium regulation, a premium based on average cost rewards attracting healthy members. Van de Ven and Ellis explain that without adequate risk adjustment, competing plans have incentives to avoid people with predictable losses and select profitable ones. Risk adjustment applies actuarial prediction to payment. Expected cost is predicted from age, sex, diagnoses and similar factors, and funds shift towards plans with costlier members. A simple form is $R_j = B \times s_j$, where $R_j$ is the payment for member $j$, $B$ is the base payment for a member of average expected cost and $s_j$ is the member's predicted cost relative to the average. In the United States, actuaries who apply health status based risk adjustment models are guided by Actuarial Standard of Practice No. 45, The Use of Health Status Based Risk Adjustment Methodologies.

Actuarial value measures plan generosity. In US federal regulation (45 CFR 156.20) it is the share of the total allowed cost of covered benefits that a plan is expected to pay for a standard population under its cost-sharing rules, as shown below.

$$AV = \frac{\text{expected plan-paid cost}}{\text{expected total allowed cost}}$$

where both terms refer to the same standard population and benefits, and the gap between them is the expected cost sharing paid by members. Under 45 CFR 156.140, bronze, silver, gold and platinum plans are set at actuarial values of 60%, 70%, 80% and 90%, each with a permitted range of variation. Actuarial value is an average over a standard population, so a member with heavy use may have far more than that share covered.

Where actuarial estimates enter health policy analysis

Actuarial analysis asks whether a scheme can afford a set of commitments; whether those commitments are good value is a question for economic evaluation. Health economists meet actuarial estimates in three main places.

Costing benefit packages. Adding or removing a service changes expected claims through its utilisation rate and unit cost, the method the ILO compendium sets out for projecting the spending of statutory schemes and the contribution rates needed to fund them.

Fiscal cost of coverage changes. The US Congressional Budget Office describes its HISIM2 model as a microsimulation that calculates expected health spending and premiums for each person in its sample, and uses it to estimate how proposed policies change coverage, which then forms the basis for their estimated effect on the federal budget.

National spending projections. The Office of the Actuary at the Centers for Medicare and Medicaid Services produces annual projections of US health spending by source of funds and type of service, work close to actuarial projection.

All three must allow for behaviour. Pauly argued that insurance lowers the price of care at the point of use, so an insured person is not prompted to restrain use when the cost is spread over all purchasers. Because of this moral hazard, use observed under less generous cover understates use under more generous cover.

Worked example of adding physiotherapy to a benefit package

The figures are illustrative. A scheme with 200,000 members is costing a course of outpatient physiotherapy as a new benefit, with 20% member coinsurance, a proportional loading of 10% and no fixed loading.

1. Expected use. Comparable data show 40 courses per 1,000 members a year when members paid in full. Allowing for induced use, the analyst assumes a rise of a quarter, to 50 per 1,000, so $f = 0.05$ courses per member per year.

2. Net premium. The allowed cost is £300 per course, of which the scheme pays 80%, or £240 per course. The net premium is then as follows.

$$P = 0.05 \times 240 = 12$$

where $P$ is the expected cost to the scheme in pounds per member per year. Members bear the other £3 (0.05 × 60) through coinsurance.

3. Gross premium. With $\beta = 0$ and $\gamma = 0.10$, the gross premium addition is as follows.

$$G = \frac{12 + 0}{1 - 0.10} = 13.33$$

where $G$ is the addition to the gross premium in pounds per member per year. Expected claims are £2.4 million a year (200,000 × 12 = 2400000) and the premium addition raises about £2.67 million.

4. Predictability. If each member has either no course or one course costing the scheme £240, with probability 0.05, the standard deviation of one member's annual cost is as follows.

$$\sigma = 240 \times \sqrt{0.05 \times 0.95} = 52.31$$

where $\sigma$ is in pounds. For the average across 200,000 members, the standard deviation is as follows.

$$\frac{52.31}{\sqrt{200000}} = 0.117$$

where the result is the standard deviation of the average cost per member in pounds, about 1% of the expected £12. In a scheme of 2,000 members the same calculation gives £1.17, nearly 10%. For the large scheme the real uncertainty lies in the assumptions. Varying induced use from none to a half moves the net premium from £9.60 to £14.40.

Assumptions that drive the estimate

Actuarial results are only as good as their assumptions, several of which are judgements. Anyone borrowing actuarial inputs for an economic model should check how each was handled.

Past claims reflect past prices, cover and members, and need adjusting before they describe a new benefit or population. Trend assumptions for prices and use compound over time and can dominate long-range estimates. Induced use sets how much more generous cover raises spending. Where cover is voluntary, adverse selection can make joiners costlier than the population average. Loadings and margins are business or policy choices. Professional standards govern what must be considered and disclosed. In the United States these are the Actuarial Standards Board's standards of practice, and in the United Kingdom the Financial Reporting Council's Technical Actuarial Standard 100 (version 2.0, effective 1 July 2023), which applies to technical actuarial work within its scope and must be applied by all members of the Institute and Faculty of Actuaries.

Actuarial analysis beside economic evaluation

Actuarial analysis overlaps with methods health economists already use, and the differences lie in the question and perspective. Budget impact analysis is the closest. The ISPOR task force lists its main elements as the size of the eligible population, the current and expected mix of treatments, the cost of those mixes and any change in condition-related costs. An actuarial costing of a new benefit asks a similar question for an insurer or fund but goes on to price it into premiums with loadings and margins, checked against the scheme's own claims. Cost-effectiveness analysis asks about health gained per unit of cost and does not address solvency.

Within insurance, community rating charges one premium across a community while risk rating varies it with assessed risk; both rest on actuarial estimates. An actuarially fair premium equals expected claims with no loading, which is different from the US regulatory actuarial value, a percentage of allowed cost. The actuarial method of survival analysis shares the name but is a life-table estimator of survival from grouped follow-up data, with no direct role in pricing.

Limitations and common misreadings of actuarial estimates

The most common misreading is to treat an expected cost as a forecast. It is an average across possible outcomes, and the actual cost in a small scheme or for a rare, expensive benefit can differ greatly, so estimates should come with their assumptions and a range.

A second error is to equate an actuarially sound premium with an affordable or fair one. A risk-rated premium can match expected claims exactly and still be out of reach for people with chronic illness, which is one reason many systems pool risk through taxes or income-related contributions. Actuarial soundness is a statement about a fund's finances, and access and equity have to be judged separately.

Third, claims data record only care that was paid for, so excluded services, care forgone because of cost sharing and unpaid recent claims are all missing. Finally, risk scores and actuarial values are averages for groups and plans, so neither predicts what any one member will pay or receive.

Sources

• Actuarial Standards Board. Actuarial Standard of Practice No. 5: Incurred Health and Disability Claims (Doc. No. 186). Washington, DC: ASB; 2017. Sections 1.2, 2.5 and 2.17. https://www.actuarialstandardsboard.org/wp-content/uploads/2017/04/asop005_186.pdf
• Actuarial Standards Board. Actuarial Standard of Practice No. 45: The Use of Health Status Based Risk Adjustment Methodologies (Doc. No. 164). Washington, DC: ASB; effective 2012. Section 1.2. https://www.actuarialstandardsboard.org/wp-content/uploads/2014/02/asop045_164.pdf
• Arrow KJ. Uncertainty and the welfare economics of medical care. American Economic Review. 1963;53(5):941-973.
• Banthin J, Hendel K, Hopkins B, Kim G, Minicozzi A, Molloy E, Percy A. Sources and Preparation of Data Used in HISIM2, CBO's Health Insurance Simulation Model. Working Paper 2019-04. Washington, DC: Congressional Budget Office; 2019. https://www.cbo.gov/publication/55087
• Centers for Medicare and Medicaid Services, Office of the Actuary. National Health Expenditure Projections. Accessed 1 October 2026. https://www.cms.gov/data-research/statistics-trends-and-reports/national-health-expenditure-data/projected
• Cichon M, Newbrander W, Yamabana H, Weber A, Normand C, Dror D, Preker A. Modelling in Health Care Finance: A Compendium of Quantitative Techniques for Health Care Financing. Geneva: International Labour Office; 1999. Chapters 2, 5, 6 and 7; Issue Brief 3. https://www.ilo.org/sites/default/files/wcmsp5/groups/public/@ed_protect/@soc_sec/documents/publication/wcms_209903.pdf
• Financial Reporting Council. Technical Actuarial Standard 100: General Actuarial Standards, version 2.0. London: FRC; 2023. https://www.frc.org.uk/library/standards-codes-policy/actuarial/tas-100/
• Pauly MV. The economics of moral hazard: comment. American Economic Review. 1968;58(3):531-537.
• Sullivan SD, Mauskopf JA, Augustovski F, et al. Budget impact analysis: principles of good practice. Report of the ISPOR 2012 Budget Impact Analysis Good Practice II Task Force. Value in Health. 2014;17(1):5-14. doi:10.1016/j.jval.2013.08.2291
• United States Code of Federal Regulations. Title 45, sections 156.20 and 156.140 (actuarial value and levels of coverage). Current text, accessed 1 October 2026. https://www.law.cornell.edu/cfr/text/45/156.140
• Van de Ven WPMM, Ellis RP. Risk adjustment in competitive health plan markets. In: Culyer AJ, Newhouse JP, eds. Handbook of Health Economics, Vol. 1A. Amsterdam: Elsevier; 2000:755-845.