Actuarium
Gold loss-development curves and a widening fan of uncertainty on navy

For students, analysts & credentialed actuaries

The working reference for decisions under uncertainty.

Actuarium pairs a team of specialist AI actuaries with verified calculators, a rigorous library, and a single unified decision method — for pricing, reserving, forecasting, reinsurance, and any choice made before the outcome is known.

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The master equation

S(a)=(1−ω)[(1−ε) ⁣∫0∞ ⁣g(PZ{u(Xa)>t}) dt+εmin⁡su(xa,s)]−ω R(a)\mathcal{S}(a)=(1-\omega)\Big[(1-\varepsilon)\!\int_0^\infty\! g\big(P_{Z}\{u(X_a)>t\}\big)\,dt+\varepsilon\min_{s}u(x_{a,s})\Big]-\omega\,\mathcal{R}(a)

Set g=id, ε=ω=0, u(x)=xg=\mathrm{id},\ \varepsilon=\omega=0,\ u(x)=x and it is expected value; turn the dials and it becomes utility, TVaR, credibility, or minimax regret.

Everything an actuarial team does — done rigorously.

Six actuarial agents

Pricing, Reserving, Forecasting, Risk & Reinsurance, Data, and a Chief-Actuary mentor. Each shows its work in LaTeX and tables, states assumptions, and cites the standards.

Meet the agents

Verified calculators

Chain-ladder with Mack errors, Bornhuetter–Ferguson, bootstrap ranges, rate indications, WC experience mods, credibility, aggregate loss, risk measures, life tables.

Open the calculators

The Library

Foundations to advanced practice: ratemaking, Workers' Compensation, reserving, stochastic methods, reinsurance, capital, data and professionalism — every formula rendered.

Browse the library

Decisions under uncertainty

The Actuarium Decision Engine: one coherent method in which expected value, utility, credibility, TVaR, minimax regret and robust Bayes are all special cases.

Explore the method

Exam pathway

CAS, SOA and CPCU roadmaps mapped to every article and tool, with a week-by-week study-plan builder and a mentor that drills you.

Plan your exams

Standards-aware by design

Agents and articles reference ASOP 23, 41, 43, 53 and 56, NCCI and ISO practice, and the CAS/SOA syllabi — so what you learn here is what the profession expects.

The team

Built around the real responsibilities of a commercial casualty actuarial function, with Workers' Compensation depth throughout.

Open the agents

Ratemaking Actuary

Pricing & Product

Rate adequacy, loss trends, WC class ratemaking, experience & schedule rating.

Reserving Actuary

Reserving & Loss Analytics

Development triangles, chain-ladder, BF, Cape Cod, Mack, bootstrap, reserve adequacy.

Financial Planning Actuary

Forecasting & Financial

Premium, loss & combined-ratio forecasts, budgets, plan-vs-actual, segment profitability.

Risk & Reinsurance Actuary

Risk & Reinsurance

Reinsurance structures, exposure rating, cat & stress testing, capital and risk measures.

Actuarial Data Scientist

Data & Analytics

SQL, Python/R, data validation, GLMs, dashboards, data-quality initiatives.

Chief Actuary & Mentor

Communication & Mentor

Executive memos, methodology documentation, ASOP compliance, CAS exam coaching.

24/7 one-to-one actuarial tutor

Socratic Tutor

Any topic, any hour: reasons step by step, checks every number with a calculator, and makes you do the thinking.

Every formula, rendered and explained.

From the chain-ladder factor to the Mack mean-squared error, the Bühlmann credibility weight, and the Wang transform — Actuarium renders mathematics natively so notation is never a barrier.

Read the librarySee the decision engine

Chain-ladder factor

f^k=∑i=1n−kCi,k+1∑i=1n−kCi,k\hat f_k=\frac{\sum_{i=1}^{n-k} C_{i,k+1}}{\sum_{i=1}^{n-k} C_{i,k}}

Bornhuetter–Ferguson

U^iBF=Ci,n−i+1+U^i0(1−1CDFn−i+1)\hat U_i^{BF}=C_{i,n-i+1}+\hat U_i^{0}\Big(1-\tfrac{1}{\mathrm{CDF}_{n-i+1}}\Big)

Bühlmann credibility

Z=nn+K,K=EPVVHMZ=\frac{n}{n+K},\qquad K=\frac{\mathrm{EPV}}{\mathrm{VHM}}

Tail value-at-risk

TVaRα(X)=11−α∫α1VaRu(X) du\mathrm{TVaR}_\alpha(X)=\frac{1}{1-\alpha}\int_\alpha^1 \mathrm{VaR}_u(X)\,du
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