1. Life contingencies (4 h.)
Basic financial mathematics: effective and nominal interest rates, financial annuities. Future lifetime as a key random variable. Survivorship functions. The force of mortality. Analytical distributions of death. Probability of death for fractions of a year. Empirical mortality tables. (Skałba chap. 2; Bowers chap. 3; Wiśniewski chap. 1)
2. Net present value of a life and endowment contract (4 h.)
Amount payable at death as a random variable. Elementary life and endowment contracts. Continuous vs. discrete model. Variable life policies. Recursive formulae. (Skałba chap. 3; Gerber chap. 3; Bowers chap. 4; Wiśniewski chap. 2)
3. Net present value of a life annuity (4 h.)
Main types of life annuities. Continuous vs. discrete model. Annuities with payments made m times in a year. Variable annuities. Actuarial equivalence equations for life and annuities contracts. Commutations functions. (Skałba chap. 4; Gerber chap. 4; Bowers chap. 5; Wiśniewski chap. 3)
4. Annuitization of net single premiums (4 h.)
Policy loss function and actuarial equivalence principle. Continuous vs. discrete model of premium payments. Premiums payed m times a year. A general type of life insurance. (Skałba chap. 5; Gerber chap. 5; Bowers chap. 6; Wiśniewski chap. 4)
5. Net premium reserves (4 h.)
Prospective vs. retrospective concept of reserves. Recursive formulae of reserves. Sum at risk and survival risk. Universal life contracts and conversion of an insurance. Technical gain of a policy year and its allocation. Policies linked to investment fund units. Commutation formulae for premiums and reserves. (Skałba chap. 6; Gerber chap. 6; Bowers chap. 7; Wiśniewski chap. 5)
6. Gross premiums and reserves (3 h.)
Basic types of expense loading. The expense-loaded premiums. Gross premium reserves. Zillmer’s approach to acquisition costs. Gross reserve vs insurer’s gain. Allocation of investment gains to policy. Policy’s cash value. Actuarial equivalence by policy alternations and conversions. (Skałba chap. 9; Gerber chap. 10; Wiśniewski chap. 6)
7. Extra mortality risks (2 h.)
A constant addition to the force of mortality. A proportional addition to the force of mortality. Risks operating at specific point of time. (Wiśniewski chap. 7)
8. Multiple-life insurance (4 h.)
Multiple-life statuses. The joint-life status. The last-survivor status. Premium formulae for the joint-life and the last-survivor status. The Schuette-Nesbitt formula. The general symmetric status of k survivors. Asymmetric statuses. Relevant examples of multiple life contracts: reversions and orphan’s annuities. (Skałba chap. 8; Gerber chap. 8; Bowers chap. 9)
9. Multiple-decrement model (3 h.)
The remaining lifetime of the current status under the multiple-decrement model of mutually exclusive decriments. Forces of decriments. Continouos vs. discrete model. Multiple-decriments tables. Decrements for fractions of a year. Premiums and reserves in the multiple-decriments insurance. (Skałba chap. 7; Gerber chap.7; Bowers chap. 9)
Szacunkowy nakład pracy studenta:
Typ aktywności K (kontaktowe) S (samodzielne)
wykład (zajęcia) 15 0
ćwiczenia (zajęcia) 15 0
egzamin 3 0
konsultacje 15 0
przygotowanie do ćwiczeń 0 20
przygotowanie do wykładów 0 0
przygotowanie do kolokwium 0 10
przygotowanie do egzaminu 0 10
… 0 12
Razem 48 52 = 100