Exam FAM – Fundamentals of Actuarial Mathematics

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SOA (Society of Actuaries) の学習者向けの無料Exam FAM – Fundamentals of Actuarial Mathematics学習ノート。各章のリンクから、要点・例題・練習問題への導線にアクセスできます。

Short-Term Insurance and Reinsurance Coverages

Types of coverage modifications for short-term insurance
Calculating the impact of coverage modifications
Loss elimination ratio and the effect of inflation on losses
Proportional and excess of loss reinsurance
Allocation of claim amounts between insurer and reinsurer

Severity, Frequency, and Aggregate Models

Severity model moments and percentiles
Scale and shape parameters in continuous severity models
Classes of severity distributions and their relationships
Characterizing distributions by existence of moments
Parameters of the (a,b,0) and (a,b,1) frequency classes
Recognizing the (a,b,0) and (a,b,1) classes and their relationships
Calculations for the (a,b,0) and (a,b,1) classes
Selecting appropriate frequency distributions
Collective and individual risk models
Normal and log-normal approximation of aggregate losses
Convolution method and stop-loss insurance expected payment
Value at Risk, Tail Value at Risk, and risk measure properties

Parametric Estimation

Maximum likelihood estimation for severity and frequency distributions
MLE with complete, individual data
MLE with complete, grouped data
MLE with truncated or censored data

Introduction to Credibility

The concept of credibility
Limited fluctuation (classical) credibility

Pricing and Reserving for Short-Term Insurance Coverages

Estimating outstanding claims: Expected Loss Ratio, Chain-Ladder, and Bornhuetter-Ferguson
Objectives of ratemaking and ratemaking data
Adjustments to ratemaking data: development, trend, and premium on-leveling
Expenses and the profit and contingencies loading in ratemaking
Overall average rates and rate changes: loss cost and loss ratio methods

Option Pricing Fundamentals

Cash flows and characteristics of puts and calls
The binomial option pricing model
The Black-Scholes formula and delta hedging
Put-call parity

Long-Term Insurance Coverages and Retirement Financial Security Programs

Insurable interest
Long-term life and health insurance coverages
Annuities
Defined benefit and defined contribution pension plans

Mortality Models

Parametric survival models and life tables
Survival and mortality probabilities from a parametric survival model
Standard actuarial notation for future lifetime distributions
Survival and mortality probabilities from a life table with fractional age assumptions
Select life tables

Present Value Random Variables for Long-Term Insurance Coverages

Present value random variables for life insurance, endowment, and annuities
Probabilities, means, variances, and covariances of the present value random variables
Relationships between insurance, endowment, and annuity present value random variables
Effect of changes in mortality and interest assumptions
Standard actuarial notation for expected values

Premium and Policy Value Calculation for Long-Term Insurance Coverages

Future loss random variables for life insurance and annuities
Premiums by the equivalence principle, portfolio percentile principle, and expected present value of profit
Gross, net, and modified net premium policy values
Effect of changes in mortality and interest assumptions
Modelling extra risk: age rating and adjustments to mortality

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