Mathematics

Stochastic Modeling in Economics and Finance by Jitka Dupačová, Jan Hurt, Josef à těpán (auth.)

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

Partially I, the basics of monetary considering and common mathematical tools of finance are awarded. the tactic of presentation is easy sufficient to bridge the weather of economic mathematics and intricate versions of economic math constructed within the later components. It covers features of money flows, yield curves, and valuation of securities.
Part II is dedicated to the allocation of cash and threat administration: classics (Markowitz thought of portfolio), capital asset pricing version, arbitrage pricing conception, asset & legal responsibility administration, price in danger. the strategy clarification takes into consideration the computational aspects.
Part III explains modeling facets of multistage stochastic programming on a comparatively obtainable point. It contains a survey of current software program, hyperlinks to parametric, multiobjective and dynamic programming, and to chance and data. It makes a speciality of scenario-based issues of the issues of state of affairs new release and output research mentioned intimately and illustrated inside a case learn.

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Additional info for Stochastic Modeling in Economics and Finance

Example text

Suppose that the cash flow of the usual coupon bond is CF, = (C,. . ,C, C F ) and that of the amortized bond CF, = (C*,. . ,C*), both of the same length. As an exercise, find C* such that the two bonds are equivalent in the sense of the equality of their present values under the valuation interest rate equal to the coupon rate c = C / F . Remind that an amortized bond is less risky than a classical coupoll bond (it immediately repays the principal) and hence, in practise, the risk premium offered by the issuer is not as high as in case of the usual coupon bond.

A . This may be accepted as true for a one-period prospective, in the above case for one year ahead. The extension to more than one period needs some kind of speculation, l~owever. Some regression techniques for a trend investigation may be helpful in this case. 4 STOCHASTIC MODELING IN ECONOMICS AND FINANCE Remark (The Distribution of R and Related Quantities) The sin~plestassumption in accordance with the random walk hypothesis is that the R's are iid and moreover that they are normally distributed.

Suppose that we have N comparable fixed or zero coupon bonds 1, ... ,N with maturities TI, . . ,TNand observed yields yl, . . , y ~ respectively. ) 1. FUNDAMENTALS 37 where the hypothetical yield curve g of a known analytical form depends on an unknown vector parameter 0 which is to be estimated, and en are disturbances with zero means. ). There is also a variety of possible choices for the analytical form of g. Having the estimate 0 , we may estimate the yield for a nonobserved maturity T # Tn,n = 1 , .

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