IFoA CS2 study plan

Define the core CS2 modelling vocabulary: state variables, transition intensities, and cash-flow functions, and write one-sentence definitions in your own words

Derive the time-inhomogeneous Markov transition probability from the Kolmogorov forward equations for a two-state model without referring to notes

Set up and solve a three-state Markov jump process (healthy, sick, dead) numerically using a small time step, and verify the rows sum to one

Build a reusable spreadsheet or Python template that takes a transition-intensity matrix and returns probabilities over a time grid

Formulate the Thiele differential equation for a multi-state life insurance policy and state each boundary condition explicitly

Compute expected present values of benefits and premiums for a disability-income contract with at least three states

Distinguish the forward and backward approaches to solving policy values, and implement one of them end to end

Explain how the equivalence principle fixes the premium in a multi-state model and verify it numerically

Derive maximum likelihood estimators for transition intensities from continuously observed data and from snapshot (censored) data

Construct the expected information matrix for a simple two-state model and obtain standard errors for the intensity estimates

Simulate survival data from a known intensity and confirm your estimator recovers the true parameter within its standard error

Identify the bias introduced by discretising observation times and quantify it in a small simulation

Derive the distribution of the time to the first jump in a time-homogeneous Markov process and connect it to the exponential waiting time

Compute the probability of eventual absorption in each absorbing state for a given generator matrix

Apply the Chapman-Kolmogorov relation to check the consistency of a computed probability matrix

Solve a small system of linear equations to obtain expected sojourn times in transient states

Extend the multi-state framework to include a dependent risk factor and describe how transition intensities become proportional hazards

Fit a Cox proportional hazards model to simulated data and interpret the coefficients in actuarial terms

Compare a parametric intensity model with a semi-parametric hazard model on the same dataset and justify a choice

Explain how frailty or unobserved heterogeneity changes observed mortality and demonstrate the effect by simulation

Build a profit-testing model for a multi-state contract that projects cash flows, reserves, and profit signatures year by year

Compute the internal rate of return and the net present value of the projected profit stream

Run one-way sensitivity analyses on the key assumptions and rank their impact on the profit signature

Reconcile a projected reserve roll-forward, explaining each component of the change

Assemble a single reference document linking each syllabus outcome in the modelling domain to the formula, method, and a worked example

Redo your weakest three topics from earlier weeks without notes and log the errors you make

Practise explaining a multi-state model derivation aloud in under five minutes, as you would in a written exam answer

Identify the two calculation types that cost you the most time and drill each until you beat a target time

Complete two full-length mock papers under exam conditions within the allotted time

Mark each mock strictly against the official mark scheme and record marks lost by cause: method, arithmetic, or interpretation

Re-derive from memory the five results you most often got wrong across all eight weeks

Finalise a one-page exam-day checklist of formulas, common traps, and time allocations per question