Some problems of Discrate Stochastic Finanacial Mathematics

Author: Natela Bokhashvili
Keywords: Financial, Stochastic, Option, Arbitrage
Annotation:

In this paper is considered the problems of stochastic financial mathematics in case of discrete times. In particular, in case of binomial model of financial (B, S) –market, it deals with the solution of the European and American types of Options Pricing Tasks; For self-financing strategies, the financial market's negativity and integrity issues are discussed. In the research section one particular model of the discrete financial market with k bonds one stock is studied. The interest rate dependent on time and related martingale measure are constructed. The relationship between martingale measure, arbitrage and completeness of financial market is established, results derived from those relations are known as fundamental theorems of stochastic financial mathematics. An illustrative two-step numerical example of calculation of the European call option is given.

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