Risk Theory I (ACTL40002)

HonoursPoints: 12.5On Campus (Parkville)

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Overview

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Semester 1
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Topics considered in this subject include premium principles, including variance principle, Esscher principle, risk adjusted principle; applications of utility theory, premium calculation and optimal reinsurance retention levels; reinsurance problems; stochastic ordering; comparisons of random losses in terms of risk measures; ruin theory, explicit solutions for the probability of ultimate ruin, the effect of reinsurance on ruin probabilities.

Intended learning outcomes

On completion of this subject, students should be able to:

  • Apply relevant pre-requisite knowledge of mathematics, probability theory and statistics in the solution of a range of practical problems;
  • Demonstrate a deep understanding of utility theory and apply them to insurance problems;
  • Describe modern premium calculation principles and show whether a premium calculation principle satisfies certain properties;
  • Design the optimal reinsurance for the insurer and the reinsurer under different optimality criterion;
  • Describe the effect of reinsurance arrangements on ruin probabilities;
  • Derive explicit solutions for the ruin probability in the classical risk model;
  • Compare tail variabilities of random losses using commonly used risk measures.
  • Analyse and assess risks using stochastic orderings.

Generic skills

  • High level of development: written communication; problem solving; statistical reasoning; application of theory to practice; interpretation and analysis.

Last updated: 4 March 2025