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Free Practice Questions for PAI TA2 — Teori Risiko

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Key Facts: PAI TA2 — Teori Risiko Exam

30

Multiple-choice questions on the TA2 paper

PAI Kurikulum Pendidikan 2024

3 hours

TA2 examination time

PAI Kurikulum Pendidikan 2024

20–25%

Syllabus weight of each of model construction and credibility theory

PAI Kurikulum Pendidikan 2024

19 August 2026

Scheduled TA2 sitting (13.30–16.30)

PAI Jadwal, Tempat dan Biaya Ujian

PAI TA2 is a 3-hour, closed-book paper of 30 multiple-choice questions in risk theory, part of the ASAI qualification. The 2024 syllabus gives the most weight to constructing and selecting parametric models and to credibility theory (20–25% each), with the rest on loss distributions, aggregate models, risk measures, simulation and chain ladder or Bornhuetter-Ferguson reserving. Only scientific calculators are allowed and PAI does not publish a pass mark. These 100 free questions are an independent English-language MCQ study adaptation.

Sample PAI TA2 — Teori Risiko Practice Questions

Try these sample questions to review concepts for the PAI TA2 — Teori Risiko exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A Pareto distribution has survival function S(x) = [θ/(x + θ)]^α with α = 3 and θ = 2,000. What is the mean excess loss e(d) = E[X − d | X > d] at d = 1,000?
A.1,000
B.1,500
C.2,000
D.3,000
Explanation: For a two-parameter Pareto with α > 1, the mean excess loss is linear in d: e(d) = (θ + d)/(α − 1). At d = 1,000, e(1,000) = 3,000/2 = 1,500. An increasing mean excess loss is a sign of a heavy tail.
2Ground-up losses X follow a Weibull distribution with S(x) = exp[−(x/500)^0.5]. Uniform inflation of 21% applies next year. What is the survival function of the inflated loss 1.21X?
A.exp[−(x/550)^0.5]
B.exp[−(x/605)^0.5]
C.exp[−(x/500)^0.605]
D.exp[−(x/732.05)^0.5]
Explanation: The Weibull is a scale family: multiplying by c keeps the shape τ and multiplies the scale θ by c. So 1.21X is Weibull with θ = 1.21 × 500 = 605 and τ = 0.5, giving S(x) = exp[−(x/605)^0.5].
3Losses X are lognormal with μ = 6.0 and σ = 0.8. Using z_0.90 = 1.282, what is the 90th percentile of X?
A.1,125.1
B.916.4
C.403.4
D.1,935.3
Explanation: ln X is normal with mean 6.0 and standard deviation 0.8, so its 90th percentile is 6.0 + 1.282 × 0.8 = 7.0256. Percentiles are preserved by the exponential transformation, so x_0.90 = e^7.0256 ≈ 1,125.1.
4A gamma distribution has shape α = 2 and scale θ = 200. What is its variance?
A.40,000
B.80,000
C.160,000
D.400
Explanation: For a gamma distribution with shape α and scale θ, E[X] = αθ and Var(X) = αθ^2 = 2 × 200^2 = 80,000.
5Claim severity X follows an inverse exponential distribution with F(x) = exp(−θ/x) for x > 0 and θ = 100. What is the median of X?
A.69.31
B.100.00
C.144.27
D.The median does not exist because the mean is infinite
Explanation: The median m solves exp(−θ/m) = 0.5, so θ/m = ln 2 and m = 100/0.693147 ≈ 144.27.
6A severity distribution is a mixture: with probability 0.70, X is exponential with mean 100; with probability 0.30, X is exponential with mean 1,000. What is E[X^2]?
A.614,000
B.314,000
C.1,400,000
D.2,000,000
Explanation: Moments of a mixture are the weighted moments of its components. An exponential with mean θ has E[X^2] = 2θ^2, so E[X^2] = 0.70 × 20,000 + 0.30 × 2,000,000 = 14,000 + 600,000 = 614,000.
7Which of these distributions has a hazard rate that decreases to 0 as x grows, indicating a heavy tail?
A.Exponential
B.Pareto
C.Normal
D.Weibull with shape τ = 2
Explanation: For a Pareto distribution the hazard rate is h(x) = α/(x + θ), which falls to 0 as x grows. A decreasing hazard rate means large losses become relatively more likely given survival, a feature of heavy-tailed distributions.
8X is exponential with mean 1. What is the distribution of Y = 200 × X^(1/3)?
A.Weibull with S(y) = exp[−(y/200)^3]
B.Weibull with S(y) = exp[−(y/200)^(1/3)]
C.Exponential with mean 200
D.Pareto with θ = 200 and α = 3
Explanation: S_Y(y) = P(200X^(1/3) > y) = P(X > (y/200)^3) = exp[−(y/200)^3]. Raising an exponential variable to the power 1/τ and multiplying by θ produces a Weibull distribution with scale θ and shape τ, here θ = 200 and τ = 3.
9A claim count N is in the (a, b, 0) class, with p_k = (a + b/k)p_(k−1) for k = 1, 2, ..., and a = 0.25, b = 0.75. Which distribution is N, and what is its mean?
A.Poisson with mean 1.00
B.Binomial with mean 0.60
C.Negative binomial with mean 1.33
D.Geometric with mean 0.75
Explanation: a > 0 identifies a negative binomial, with a = β/(1 + β) and b = (r − 1)β/(1 + β). From a = 0.25, β = 1/3; then (r − 1) × 0.25 = 0.75 gives r = 4. The mean is rβ = 4/3 ≈ 1.33.
10In the (a, b, 0) recursion p_k/p_(k−1) = a + b/k, which condition identifies a binomial distribution with m trials?
A.a = 0 and b > 0
B.a > 0 and a + b > 0
C.a < 0 and −b/a = m + 1 for a positive integer m
D.a > 0 and b = 0
Explanation: For a binomial with m trials and probability q, a = −q/(1 − q) < 0 and b = (m + 1)q/(1 − q). So −b/a = m + 1, which makes p_(m+1) = 0 and ends the distribution at m.

About the PAI TA2 — Teori Risiko Exam

TA2 Teori Risiko (formerly A70) is the short-term actuarial mathematics module of the professional examinations run by Persatuan Aktuaris Indonesia (PAI) and one of the ASAI-level modules. Under the 2024 syllabus it is a 3-hour, closed-book paper of 30 multiple-choice questions on non-life actuarial models: severity and frequency models, coverage modifications, aggregate losses, risk measures, fitting and selecting parametric models, credibility, simulation and outstanding claims estimation. This free bank is an independent English-language MCQ study adaptation, not an official translation or simulation of the PAI paper, which is set in Indonesian.

Exam sponsor: Persatuan Aktuaris Indonesia (PAI). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

A 3-hour closed-book paper of 30 multiple-choice questions covering nine sections: severity models (5–10%), frequency models (5–10%), coverage modifications (5–10%), aggregate models (10–15%), risk measures (2.5–5%), construction and selection of parametric models (20–25%), credibility theory (20–25%), simulation (5–10%) and estimation of outstanding claims (5–10%). Only non-programmable scientific calculators are permitted. In 2026 PAI held a May sitting and scheduled TA2 for 19 August 2026, 13.30–16.30, in Jakarta, Bandung, Yogyakarta and Surabaya.

Time Limit

3 hours (180 minutes)

Passing Score

Not published by PAI

Exam / Certification Fees

Rp1,500,000 (registration 6–20 July 2026) or Rp2,000,000 (21–24 July 2026); students and ministry candidates Rp300,000 or Rp800,000

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

8 of 100 questions

Severity Models

Pareto, Weibull, lognormal, gamma and inverse exponential distributions, mixtures, transformations, hazard rates and mean excess loss.

8 of 100 questions

Frequency Models

(a, b, 0) and (a, b, 1) classes, zero-truncated and zero-modified distributions, gamma mixtures of Poissons and exposure changes.

8 of 100 questions

Coverage Modifications

Ordinary and franchise deductibles, coinsurance, limits and layers, loss elimination ratio, Poisson thinning and inflation leverage.

12 of 100 questions

Aggregate Models

Individual and collective models, compound Poisson and negative binomial variances, Panjer recursion, stop-loss premiums and normal approximation.

4 of 100 questions

Risk Measures

Coherence, why VaR can fail subadditivity, and VaR and TVaR calculations.

22 of 100 questions

Construction and Selection of Parametric Models

Method of moments, percentile matching, maximum likelihood with censored and truncated data, delta method, MSE, Bayesian estimation, likelihood ratio tests, AIC and SBC, and Kolmogorov-Smirnov and p-p diagnostics.

22 of 100 questions

Credibility Theory

Limited fluctuation standards, Bühlmann and Bühlmann-Straub models, exact credibility, and nonparametric and semiparametric empirical Bayes estimation.

8 of 100 questions

Simulation

Inversion for discrete and continuous variables, required number of simulations, bootstrap and permutation tests.

8 of 100 questions

Estimation of Outstanding Claims

Long-tail business, run-off triangles, chain ladder factors, ultimates and reserves, and the Bornhuetter-Ferguson method.

Preparing for the PAI TA2 — Teori Risiko Exam

What You Need to Know

  • Passing score: Not published by PAI
  • Assessment: A 3-hour closed-book paper of 30 multiple-choice questions covering nine sections: severity models (5–10%), frequency models (5–10%), coverage modifications (5–10%), aggregate models (10–15%), risk measures (2.5–5%), construction and selection of parametric models (20–25%), credibility theory (20–25%), simulation (5–10%) and estimation of outstanding claims (5–10%). Only non-programmable scientific calculators are permitted. In 2026 PAI held a May sitting and scheduled TA2 for 19 August 2026, 13.30–16.30, in Jakarta, Bandung, Yogyakarta and Surabaya.
  • Time limit: 3 hours (180 minutes)
  • Exam / certification fees: Rp1,500,000 (registration 6–20 July 2026) or Rp2,000,000 (21–24 July 2026); students and ministry candidates Rp300,000 or Rp800,000 Official sources

Using Our Practice Resources

  • Work through all 100 available questions
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PAI TA2 — Teori Risiko: Suggested Study Strategy

1Spend the most time on model fitting and credibility: together they carry 40–50% of the syllabus, including maximum likelihood with censored and truncated data and Bühlmann-Straub premiums.
2Know the exponential and Pareto shortcuts for deductibles, limits, mean excess loss and VaR/TVaR, because they appear inside larger questions.
3Practise Panjer's recursion and compound variance formulas by hand with a scientific calculator.
4Do not neglect simulation and reserving: inversion, bootstrap MSE, chain ladder factors and Bornhuetter-Ferguson reserves are quick marks once practised.

Frequently Asked Questions

What does PAI TA2 cover?

TA2 Teori Risiko covers non-life actuarial models under PAI's 2024 syllabus: severity and frequency models, coverage modifications, aggregate loss models, risk measures, construction and selection of parametric models, credibility theory, simulation, and estimation of outstanding claims with the chain ladder and Bornhuetter-Ferguson methods.

What is the TA2 exam format?

The syllabus specifies 30 multiple-choice questions in 3 hours. The May 2026 paper was closed-book, gave five options per question with equal weights and no deduction for wrong answers, and allowed only non-programmable scientific calculators.

How much does TA2 cost and when is it held in 2026?

PAI lists Rp1,500,000 for ASAI-level modules when registering from 6 to 20 July 2026 and Rp2,000,000 from 21 to 24 July 2026, with reduced fees of Rp300,000 and Rp800,000 for D1–D4 and S1 students and ministry candidates. TA2 is scheduled for 19 August 2026, 13.30–16.30; PAI also held a May 2026 sitting.

What is the pass mark for TA2?

PAI does not publish a numeric pass mark in its syllabus or exam guidelines. Results are announced by PAI after each sitting.

Are these official PAI exam questions?

No. This is independent practice by OpenExamPrep in English with four-option multiple-choice questions. It is not an official translation of the Indonesian paper, does not simulate its five-option format, and is not affiliated with or endorsed by PAI.