Probabilistic methods for financial payments depending on death or survival. Technical bases for life insurance. Life insurance and Premiums. "Mathematical" reserves. Measuring of expected profit. Participating policies. Unit and index linked.. Tariff Premium. Model for differential mortality and risk classification. Projected mortality models. Profit Testing. Embedded Value. Solvency and ERM for life insurance companies. Regulatory framework
The Course aims at introducing and discussing life insurance products through basic instruments of actuarial mathematics. In particular, instruments will be furnished to compute the expected value of uncertain financial operations and therefore the amount of life insurance premiums and reserves, both in traditional and innovative models. Finally, the capital requirement calculation problem for insurance portfolios will be discussed, in the light of Solvency outlines and other regulations.
Probability and mathematics for statistics
72 hours of classroom lectures.
Type of Assessment
Written and oral examination
1. Types of insurance coverage:
- personal insurance: life, damage, health...;
- collective insurance: natural catastrophes, artistic heritage risks...
2. Financial operations:
-certainty and uncertainty;
- discounted and expected values;
- price of an uncertain investment: risk aversion and risk neutrality;
3. Demographic basis for life insurance:
- life duration;
- survival function and mortality intensity;
- mortality tables;
- longevity risk.
4. Evaluation of life insurance contracts:
- life and death case policies;
- equity principle: unitary and periodic payments;
inequalities between actuarial values.
5. Mathematical reserves:
- pure reserve;
- prospective and retrospective reserve;
- computation methods;
- tarif conditions.
6. Innovative life contracts:
- flexible performance;
- indexed and re-assessed contracts;
- unit and index linked policies;
- pricing models;
- reserve computation.
7. Linked policies with guaranteed minimum:
- structured bonds;
- call and put options;
- options associated to linked policies;
- stock price model;
- computation of additional reserves.
8. From embedded to fair value:
- solvency in deterministic and stochastic framework;
market-consistent versus risk-neutral evaluation.