Actuarium

SOA SRMStatistics for Risk Modeling

Associateship (ASA)
3.5 hoursΒ·35 multiple-choiceΒ·β‰ˆ250 study hours

Syllabus learning objectives

Official syllabus

Paraphrased from the SOA syllabus so the study-plan builder and practice sets track the topics you will actually be examined on. Weights are the official topic ranges.

Basics of statistical learning

15%
  • Distinguish supervised from unsupervised learning and regression from classification problems.
  • Apply the bias-variance tradeoff and cross-validation to assess and tune model complexity.
  • Compute and interpret common model evaluation metrics (RMSE, AUC, confusion matrix, lift).
  • Describe the train/validation/test workflow and the risk of overfitting and data leakage.

Linear models

30%
  • Fit and interpret multiple linear and logistic regression models, including coefficient interpretation and significance testing.
  • Apply regularization (ridge, lasso, elastic net) to control overfitting and perform variable selection.
  • Diagnose regression assumption violations using residual plots, leverage and influence statistics.
  • Extend linear models to generalized linear models (Poisson, gamma, Tweedie) for actuarial response variables.

Time series

15%
  • Identify stationarity and apply differencing/transformations to achieve it.
  • Fit and forecast ARIMA and exponential smoothing models using ACF/PACF diagnostics.
  • Evaluate time-series model fit via residual diagnostics and out-of-sample forecast error.
  • Apply time series decomposition to separate trend, seasonal and residual components.

Principal components analysis

10%
  • Compute principal components from a covariance/correlation matrix and interpret loadings and explained variance.
  • Apply PCA for dimension reduction prior to modeling and for visualization of high-dimensional data.
  • Select the number of components using scree plots and cumulative variance explained.
  • Recognize the effect of scaling/standardization on PCA results.

Decision trees

20%
  • Grow classification and regression trees using recursive binary splitting and impurity/variance-reduction criteria.
  • Apply pruning (cost-complexity) to control tree size and avoid overfitting.
  • Fit ensembles (bagging, random forests, boosting) and interpret variable importance measures.
  • Compare tree-based methods with GLMs on interpretability, accuracy and handling of nonlinearity/interactions.

Cluster analysis

10%
  • Apply k-means and hierarchical clustering algorithms and interpret dendrograms.
  • Select an appropriate number of clusters using elbow, silhouette or gap-statistic methods.
  • Choose distance/dissimilarity measures appropriate to the data type.
  • Interpret cluster assignments for actuarial segmentation applications (e.g., risk classification).

Lecture videos for this exam

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MIT 18.650 Statistics for Applications, Fall 2016

MIT OpenCourseWare Β· Statistics & Regression Β· playlist

Overview

SRM is a multiple-choice exam based largely on An Introduction to Statistical Learning plus regression and time-series notes. It emphasizes concepts (bias–variance, cross-validation, regularization) with light computation.

Duration
3.5 hours
Questions
35 multiple-choice
Style
Computer-based
Passing
Scaled 6 of 10

Syllabus map

Basics of statistical learning
15%
Statistics and Estimation for Actuaries
Linear models
30%
Statistics and Estimation for ActuariesGLMs and Predictive Modeling in Pricing
Time series
15%
Forecasting Premium, Loss, and Profitability
Principal components analysis
10%
GLMs and Predictive Modeling in Pricing
Decision trees
20%
GLMs and Predictive Modeling in Pricing
Cluster analysis
10%
GLMs and Predictive Modeling in Pricing

Key formulas

Coefficient of determination β€…β€ŠR2=1βˆ’SSESST\;R^2=1-\dfrac{SSE}{SST}, adjusted β€…β€ŠRΛ‰2=1βˆ’SSE/(nβˆ’pβˆ’1)SST/(nβˆ’1)\;\bar R^2=1-\dfrac{SSE/(n-p-1)}{SST/(n-1)}

Logistic regression β€…β€Šln⁑p1βˆ’p=x⊀β\;\ln\dfrac{p}{1-p}=\mathbf{x}^\top\beta, p=11+eβˆ’x⊀βp=\dfrac{1}{1+e^{-\mathbf{x}^\top\beta}}

Bias–variance β€…β€ŠE[(yβˆ’f^)2]=Bias⁑2+Var⁑+Οƒ2\;E[(y-\hat f)^2]=\operatorname{Bias}^2+\operatorname{Var}+\sigma^2

PCA proportion of variance of component jj: Ξ»j/βˆ‘kΞ»k\lambda_j/\sum_k\lambda_k

Exponential smoothing β€…β€Šy^t+1=Ξ±yt+(1βˆ’Ξ±)y^t\;\hat y_{t+1}=\alpha y_t+(1-\alpha)\hat y_t

Study strategy

  1. Read ISLR chapters 2–10 actively and be able to explain every figure.

  2. Know which methods are supervised/unsupervised and parametric/non-parametric.

  3. Practice reading regression output (coefficients, standard errors, t, p, F) quickly.

  4. Memorize how each tuning parameter moves the bias–variance trade-off.

Common traps

  • Adjusted R2R^2 can fall when adding a predictor; R2R^2 never does.

  • Interpreting a logistic coefficient as a change in probability instead of log-odds.

  • Confusing k-fold CV with LOOCV bias/variance properties.

  • Assuming random forests need pruning (they do not).

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