By Jitka Dupačová, Jan Hurt, Josef à těpán (auth.)

Partly I, the basics of monetary considering and undemanding mathematical equipment of finance are provided. the strategy of presentation is easy sufficient to bridge the weather of economic mathematics and complicated types of monetary math built within the later components. It covers features of money flows, yield curves, and valuation of securities.

Part II is dedicated to the allocation of money and danger administration: classics (Markowitz thought of portfolio), capital asset pricing version, arbitrage pricing idea, asset & legal responsibility administration, worth in danger. the strategy rationalization takes into consideration the computational aspects.

Part III explains modeling points of multistage stochastic programming on a comparatively available point. It incorporates a survey of present software program, hyperlinks to parametric, multiobjective and dynamic programming, and to likelihood and records. It makes a speciality of scenario-based issues of the issues of situation iteration and output research mentioned intimately and illustrated inside of a case research.

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**Example text**

15, the bond is a discount one. The dependence of the price of the bond on time to maturity is graphically illustrated in Figure 8. 05, etc. 2 Exercise. , with frequency 2, which is perhaps the most frequent case. I. 3 51 Remark (Construction of the Yield Curve of Coupon Bonds) The silllplest way is to take a set of similar coupon bonds with different maturities and their calculated yields to maturity. Then some method of fitting discussed above may be applied. An alternative approach is known as bootstrapping.

The crossover rate IAB is defined as a solution to the equation Obviously, there may be more than one solution so that we must select that one with a reasonable economic interpretation. Since the present value is a linear function on the space of cash flows, we see that the crossover rate iABis in fact the internal rate of return determined by the difference between the two projects, I R R A - ~ : In the neighborhood of the crossover rate the investor should take care and carefully study also the sensitivity of the present value profiles with respect to the interest rate.

A crossover* rate of two projects is such an interest rate for which the present values of the two projects are equal. Formally, let us consider two projects CFA and CFB. The crossover rate IAB is defined as a solution to the equation Obviously, there may be more than one solution so that we must select that one with a reasonable economic interpretation. Since the present value is a linear function on the space of cash flows, we see that the crossover rate iABis in fact the internal rate of return determined by the difference between the two projects, I R R A - ~ : In the neighborhood of the crossover rate the investor should take care and carefully study also the sensitivity of the present value profiles with respect to the interest rate.