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Topics include collective risk model, calculation of moments and mgf of aggregate claims, recursion formulae, effect of reinsurance; individual risk model, De Pril's recursion formula; fundamentals of decision theory; credibility theory; exact credibility and the Buhlmann-Straub model; basics of ruin theory.
Intended learning outcomes
On successful completion of this subject a student should be able to:
- Explain the fundamental concepts of Bayesian statistics and apply these concepts to derive Bayesian estimators;
- Describe and apply the fundamental concepts of credibility theory;
- Derive and calculate probabilities for, and moments of, loss distributions both with and without simple reinsurance arrangements;
- Construct risk models appropriate for short term insurance contracts and derive both moments and moment generating functions for aggregate claim amounts under these models;
- Derive recursion formulae to calculate aggregate claims distributions for short term insurance contracts;
- Describe and apply approximate methods of calculating an aggregate claims distribution;
- Explain the concept of ruin for a risk model.
High level of development:
- Written communication;
- Problem solving;
- Statistical reasoning;
- Application of theory to practice;
- Interpretation and analysis.
Last updated: 18 December 2020