COURSE AIMS AND OBJECTIVES: :
The first objective is to introduce to students the basic concepts of financial mathematics such as the compound interest, the present value of a cash flow and the yield. The second and the main objective is to get students acquainted with the mathematics of life insurance. In particular, survival times, mortality tables, life annuities, premiums and reserves will be studied in detail.
COURSE DESCRIPTION AND SYLLABUS:
The following topics will be presented
1. Introduction to Financial Mathematics. Simple and compound interests. Present values. Effective and nominal interest rates. Accumulation factors and discounting. Force of interest. Deterministic and stochastic cash flows. Yields. Continuous cash flows. Annuities (due, certain, payable continuously, payable pthly, varying, etc.).
2. Mortality. Survival times and hazard function. Conditional probabilities. Force of mortality. Analytical distributions of survival times. Life tables.
3. Life insurance. Elementary insurance types. Standard types of life annuities. Net premiums. Premiums paid pthly. General type of life insurance.
4. Policy values. Premium reserve. Prospective, retrospective and recursive formula for the net premium reserve. Mortality profit.
5. Additional topics. (to be covered if time permits) Multiple life insurance. Estimation of the lifetime distribution. Censoring. Kaplan-Meier estimator. Markov models.