Dr Hao Xing COL 7.12

This course is compulsory on the MSc in Risk and Stochastics. This course is available on the MSc in Financial Mathematics and MSc in Statistics (Financial Statistics). This course is not available as an outside option.

A self-contained comprehensive introduction to life and non-life insurance mathematics. For the life insurance, mortality laws are analysed from probabilistic and statistical point of view. Actuarial analysis of basic insurance products: pure endowment, life insurance/assurance, and annuity. Prospective/retrospective reserves of these products. Extension to general multi-states policy is studied via Markov chains Pricing embedded interest and mortality guarantees is introduced. For the non-life insurance, axiomatic approach to ordering of risks is presented, optimal forms of insurance from the insured's and from the insurer's point of view are analysed, and Pareto-optimal risk exchanges are introduced. Standard schemes of reinsurance are introduced and analysed. Ruin probability of an insurance company and capital requirement are studied. Heavy tail distributions and the extreme value theory are introduced. Case studies on current developments in life and non-life insurance industry are also presented.

20 hours of lectures and 10 hours of seminars in the MT.

An informal 'open book' mid-term practice examination will take place in Week 6.

5 to 6 problem sets will be assigned.

R Norberg, Risk and Stochastics in Life Insurance (Lecture notes)

R Norberg, Non-life Insurance Mathematics (Lecture notes)

T Mikosch, Non-Life Insurance Mathematics.

Exam (100%, duration: 2 hours) in the LT week 0.