CS2 —Risk Modelling and Survival Analysis

CS2 builds directly on CS1, extending the statistical toolkit into stochastic processes, survival analysis, time series, and loss modelling — the mathematics behind mortality tables, insurance claim patterns, and the general insurance pricing cycle. It closes with a first formal introduction to machine learning, reflecting how data science techniques are increasingly used alongside traditional actuarial methods.

Under the pre-2019 exam structure, CS2’s content was split across two separate papers: CT4 (Models) and CT6 (Statistical Methods). The first twelve chapters — covering Markov chains, survival models, and mortality graduation — map to old CT4. The next eight chapters, covering time series and general insurance loss modelling, map to old CT6. The final chapter, machine learning, is new to the current curriculum and has no direct equivalent in the old syllabus.

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Chapter List — CT4 vs CT6

CT4 (Models)

  • 1. Stochastic processes
  • 2. Markov chains
  • 3. The two-state Markov model and the Poisson model
  • 4. Time-homogeneous Markov jump processes
  • 5. Time-inhomogeneous Markov jump processes
  • 6. Survival models
  • 7. Estimating the lifetime distribution
  • 8. Proportional hazards models
  • 9. Exposed to risk
  • 10. Graduation and statistical tests
  • 11. Methods of graduation
  • 12. Mortality projection

CT6 (Statistical Methods )

  • 13. Time series (1)
  • 14. Time series (2)
  • 15. Loss distributions
  • 16. Extreme value theory
  • 17. Copulas
  • 18. Reinsurance
  • 19. Risk models 1
  • 20. Risk models 2

New to Curriculum 2019 (no old-syllabus equivalent)

  • 21. Machine learning

PART 1 : — Stochastic Processes and Markov Models (Chapters 1–5)

This block introduces systems that move between different states over time — exactly how an income protection or critical illness policy needs to be modelled, as a policyholder moves between “healthy,” “sick,” and “dead” states. Markov chains and the two-state/Poisson model build the discrete-time and simplest continuous-time versions of this idea, while Markov jump processes (both time-homogeneous and time-inhomogeneous) generalise it to more realistic settings where transition rates change with age or time — the mathematical basis for multi-state health and disability insurance pricing.

PART 2 : — Survival Models and Mortality (Chapters 6–12)

Survival models formalise how to describe the future lifetime of a policyholder as a random variable — the direct extension of the life tables introduced in CM1, but built here from first statistical principles. Estimating the lifetime distribution and proportional hazards models then teach you how to actually fit these models to real (and often incomplete or “censored”) data — proportional hazards models, in particular, are how actuaries quantify the effect of a risk factor like smoking status on mortality. Exposed to risk, graduation, and mortality projection round the block off with the practical, applied side: turning raw, noisy mortality data into the smooth, usable tables that insurers and pension funds actually price and reserve with — including projecting how life expectancy will keep improving decades into the future, which is critical to pricing long-term annuities correctly.

PART 3 : — Time Series (Chapters 13–14)

Time series models describe how a quantity evolves over time when today’s value depends on yesterday’s — inflation rates, interest rates, or claim numbers are all classic examples. This is the toolkit used to forecast future claims inflation or investment returns based on historical patterns, rather than assuming they stay constant.

PART 4 : — Loss Modelling for General Insurance (Chapters 15–19)

Loss distributions model the size of individual claims (using distributions like the lognormal or Pareto), while extreme value theory focuses specifically on the tail — the rare but severe claims that drive an insurer’s worst-case scenarios, like catastrophic flood or earthquake losses. Copulas then let you model dependency between different types of risk (for example, how a single storm event can trigger correlated claims across property and motor lines simultaneously), and reinsurance covers how insurers pass some of that risk on to a reinsurer. Risk models 1 and 2 pull all of this together into aggregate claims modelling — projecting the total claims cost for an entire portfolio, which is the foundation of both pricing and capital adequacy work in general insurance.

PART 5 : —Machine Learning (Chapter 21)

The final chapter introduces core machine learning concepts — decision trees, and the general principles behind supervised learning — as they apply to actuarial work. This reflects how Indian insurers and insurtechs increasingly supplement traditional GLM-based pricing with machine learning techniques for tasks like fraud detection and more granular risk segmentation.

Exam Format

Both papers are computer-based. Paper A is a 3¼-hour computer-based exam covering a range of questions of varying marks. Paper B is a 1¾-hour computer-based practical exam using R, covering data analysis and statistical modelling problems. Both papers must be sat in the same exam sitting, with a combined mark determining the pass.

Prerequisites

CS2 assumes competence in CS1 and its underlying material. There is no formal barrier to attempting CS2 first, but the subject builds directly on CS1’s statistical foundations, so completing CS1 first is strongly recommended.