Iran Official Insurance Actuary Exam study plan

Derive the moment generating function for the exponential, gamma, normal, and Poisson families, and use it to obtain the first four moments of each distribution from memory.

Apply the law of total probability and the law of total expectation to two-stage mixture problems, and verify each answer by simulation or by a closed-form special case.

State and prove the central limit theorem conditions and use the delta method to approximate the variance of a transformed estimator.

Solve ten maximum-likelihood estimation problems covering censored exponential data, binomial proportions, and the multinomial model, and check each variance via the Fisher information.

Construct exact confidence intervals and hypothesis tests for means, variances, and proportions, including the small-sample t and chi-square cases.

Compute present and accumulated values for annuities with constant and geometrically varying payments, and derive the closed forms for increasing and decreasing annuities.

Calculate the internal rate of return, net present value, and duration for a multi-period cash flow, and explain why duration measures price sensitivity.

Distinguish between the force of interest, nominal rates with different compounding frequencies, and effective rates, and convert between them without error.

Build a complete life table from a given mortality law, and compute survival probabilities, curtate and complete expectations of life, and central death rates.

Compute net single premiums and annual net premiums for term, whole life, endowment, and deferred products using both the equivalence principle and the standard identity linking insurance to annuity values.

Reserve each of the products from the previous goal using the prospective, retrospective, and recursive (Fackler) methods, and confirm that all three agree at the same duration.

Handle fractional-age assumptions by computing values under uniform distribution of deaths and constant force of mortality, and quantify how much the choice of assumption changes the reserve.

Extend the pricing work to multi-life and contingent products, including joint-life and last-survivor annuities and reversionary annuities.

Model premium payment modes other than annual, and compute the mode loading and the loss from fractional premiums.

Analyze a with-profit or unit-linked style contract qualitatively, identifying how the reserve and the premium respond to a change in interest rate and mortality.

Explain the equivalence principle, the portfolio percentile premium principle, and the expected-value principle, and state when each is appropriate.

Estimate frequency and severity distributions from a claims triangle or claims list, and select between Poisson, negative binomial, lognormal, and Pareto severity models with a stated criterion.

Apply Bayesian credibility to a portfolio of groups, computing the credibility factor and the credibility premium under the Bühlmann and Bühlmann-Strauss models.

Derive the limited expected value and use it to handle policy limits, deductibles, and coinsurance in expected claim cost calculations.

Compute IBNR reserves using the chain-ladder method and state the assumptions that the method requires.

Derive the adjustment coefficient for the classical risk process with exponential and with gamma claim sizes, and compute the Lundberg bound on ruin probability.

Apply the Cramér-Lundberg approximation and the diffusion approximation to the same surplus process, and compare the resulting ruin probabilities.

Explain moral hazard, adverse selection, and risk classification, and evaluate how each affects the equilibrium premium in a competitive market.

Distinguish the main reinsurance forms, proportional and non-proportional, and calculate the reinsurer's share of a loss under quota share, surplus share, excess of loss, and stop loss.

Summarize the supervisory framework governing Iranian insurers, including solvency and reserve requirements, the role of the regulator, and the rules on technical provisions, at the level of principle.

Outline the structure of Iranian social security and compulsory insurance, identifying which risks are covered by the state scheme and which by the commercial market.

Prepare the key lines of an insurer's balance sheet and income statement, and explain how technical reserves and unearned premium reserves flow through them.

Explain duration matching and immunization for an insurer's asset-liability position, and compute the duration gap for a simple two-asset, one-liability example.

Apply the actuarial code of conduct to three realistic dilemmas, including a pricing instruction from management and a data quality problem, and state the correct course of action with reasons.

Document the assumptions, data, and limitations behind an actuarial estimate in a form that a peer reviewer could check independently.

Re-solve every previously missed problem across all domains under timed conditions, targeting a 75 percent or better score.

Take one full-length timed mock exam under exam conditions and review every error by domain.