Actuarial Syllabi
Sections relevant to aggregatge.
IAA
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7. ACTUARIAL MODELS
7.2 FUNDAMENTALS OF SEVERITY MODELS
7.2.1 Recognize classes of distributions, including extreme value distributions, suitable for modelling the distribution of severity of loss and their relationships. (B4)
7.2.2 Apply the following techniques for creating new distributions: multiplication by a constant, raising to a power, exponentiation, mixing. (B3)
7.2.3 Calculate various measures of tail weight and interpret the results to compare the tail weights. (B5)
7.3 FUNDAMENTALS OF FREQUENCY MODELS
7.3.1 Explain the characteristics of distributions suitable for modeling frequency of losses, for example: Poisson, mixed Poisson, binomial, negative binomial, and geometric distributions. (B2)
7.3.2 Identify applications for which each distribution may be used; explain the reasons why; and apply the distribution to the application, given the parameters. (B3)
7.4 FUNDAMENTALS OF AGGREGATE MODELS
7.4.1 Compute relevant moments, probabilities and other distributional quantities for collective risk models. (B3)
7.4.2 Compute aggregate claims distributions and use them to calculate loss probabilities. (B3)
7.4.3 Evaluate the effect of coverage modifications (deductibles, limits and coinsurance) and inflation on aggregate models. (B3)
CAS
MAS I
B. Statistics
- For the Exponential, Gamma, Weibull, Pareto, Lognormal, Beta, and mixtures thereof:
- Identify the applications to Insurance claim modeling in which each distribution is used and reasons why.
- Transformation of distributions
- Frequency, severity, and aggregate loss
- Common continuous distributions for modeling claim severity
- Mixing distributions
- Tail properties of claim severity
- Effects of coverage modifications including, for example: limits, deductibles, loss elimination ratios and effects of inflation
Part 8 Advanced Ratemaking
B. Excess, Deductible, and Individual Risk Rating
Apply frequency and severity distributions to determine expected losses by layer of insurance.
Calculate the cost of the layer of risk given the loss cost.
Estimate aggregate loss distributions.
- Construction of an aggregate loss distribution from frequency and severity distributions
Construct a loss sensitive rating plan (LSRP).
C. Catastrophic and Reinsurance Pricing
- Determine the price of various types of reinsurance contracts.
- Types of contracts, including excess of loss, quota share, surplus share, treaty, aggregate excess of loss, and facultative
- Common methods for pricing reinsurance, including burning cost, exposure rating and experience rating
- Reinsurance loss development and trend
- Use of increased limit factors in reinsurance pricing
- Evaluation of aggregate distribution models
- Prospective and retrospective pricing in reinsurance
- Reinsurer’s expenses
- Final premium
- Determine the effect of common contract provision on the price of reinsurance contracts.
- Pricing for reinstatements, loss corridors, clash, profit and sliding scale commissions, and other common provisions in reinsurance contracts
- Specify, fit, and use loss distribution based exposure curves.
- Define an exposure curve
- Limited and unlimited distributions
- Expected value and total loss probability
- Use of MBBEFD class distributions as exposure curves
Part 9
C. Financial Risk Management
- Describe various risk measures and the need for practicing sound financial risk management.
- Capital structure and risk taking incentives
- Regulation and rating agency
- Value at risk (VaR)
- Risk-based capital
- Expected policyholder deficit (EPD)
- Capital associated with a constant EPD ratio
- Risk-adjusted return on capital (RAROC), including alternative measures of income and alternative measures of risk-adjusted capital
- Economic value added (EVA)
- Percentile layer of capital
- Lessons from past failures due to poor financial risk management
- Describe the concept of economic capital (or risk capital) in the insurance industry and various methods of allocating the risk capital to business units or lines of business.
Strengths and weaknesses of the various allocation methods using risk measures such as: - Percentile (VaR) - Conditional tail expectation (CTE) - EPD Ratio - Merton-Perold method - Insolvency Put/EPD ratio risk measure - Myers-Read method - Co-Measures - Co-CTE - Percentile Layer of Capital
Apply the RAROC framework to risk management in the insurance industry.
Assess the performance of business units and set prices for insurance policies on a risk-adjusted basis
D. Rate of Return, Risk Loads, and Contingency Provision
Use Riskiness Leverage models to determine risk loads.
Calculate and compare the risk loads for property catastrophe insurance
- Order dependency
- Marginal Surplus method
- Marginal Variance method
- Sub-additive and super-additive properties
- Renewal additivity
- Shapley Value method
- Covariance Share metho
SOA
- Topic: Severity Models
- Describe how changes in the parameters affect the distributions.
- Create new distributions by multiplication by a constant, raising to a power, exponentiation, mixing and splicing.
- Understand and interpret the characteristics of severity distributions.
- Compare two distributions based on various characteristics of their tails, including moments, ratios of moments, limiting tail behavior, hazard rate functions, and mean excess functions.
- Understand the derivation and characteristics of the Generalized Extreme Value and the Generalized Pareto distributions.
- Apply the Generalized Extreme Value and the Generalized Pareto distributions to the estimation of tail measures and probabilities.
- Topic: Aggregate Models
- Use convolution and recursive formulas to derive probability and distribution functions for aggregate claims distributions with (a,b,0) or (a,b,1) frequency, and with discrete severity distributions.
- Derive the discretized version of a continuous distribution using the method of rounding and local moment matching.
- Perform calculations for sums of compound Poisson models.
- Topic: Coverage Modifications
- Evaluate the effects of the following coverage modifications: deductibles, policy limits, maximum covered loss, coinsurance, and stop loss reinsurance.
- Calculate and interpret loss elimination ratios, increased limits factors, and deductible factors.
- Evaluate and interpret the effects of inflation on losses.