Introduction to Actuarial and Financial Mathematics 1000-135WMF
Description:
1. Theory of interest: simple, compound and continuous interest, effective and nominal interest rates, discount rates.
2. Present value and future value, cash flows, accumulation process, internal rate of return.
3. Annuities with various payment schemes, loan amortization schedules.
4. Term structure of interest rates: interbank rates; zero coupon bonds, bonds with constant coupons, forward rate agreement (FRA), yield curves. Interest rate derivatives: swaps, caps, floors.
5. Immunization of bond portfolios: duration, convexity, parallel shifts of the term structure.
6. Stock market: forward and future contracts and their pricing, indices contracts, European and American options , arbitrage, hedging strategies, pricing in simple discrete models (Cox-Ross-Rubinstein model (CRR)), martingale method.
7. Elements of the survival analysis: survival function, intensity of mortality, hazard rate, classical mortality models of de Moivre, Gompertz, Mackeham; Kaplan-Meier estimator based on the mortality tables.
8. Model of the collective risk in non-life insurance: moment generating function in Poissonian models, premium calculation quantile principle, coherent measures of risk, Value at Risk (VaR), ruin theory – the Cramer-Lundberg model.
Course coordinators
Type of course
Prerequisites (description)
Assessment criteria
Examination: evaluation of the exercises based on two tests.
The final grade based on weighted scoring (50% exercises+50% examination).
Bibliography
Literature
1) Kellison, S.G. “The theory of interest”, (2008), McGraw-Hill/Irwin,
2) Jaworski P.W, Jaworska K.M., “Rynki kapitałowe (Matematyka finansowa I)”, (2011), skrypt UW dostępny online,
3) Jakubowski J., Palczewski A., Rutkowski M., Stettner Ł „Matematyka Finansowa”; (2006), Wydawnictwo WNT,
4) Bowers N. L., Gerber, H. U., Hickman J. C. et al. „Actuarial mathematics” (1997), 2nd ed.; Society of Actuaries,
5) Denuit M., Dhaene J., Goovaerts M., Kaas R. “Actuarial Theory for Dependent Risks, Measures, Orders and Models” (2005), John Wiley & Sons, Ltd,
6) Dickson D.C.M., Hardy M.R., Waters H.R. “Actuarial Mathematics for File Contingent Risks” (2009), Cambridge University Press.