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2 Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2 Medvedev G.

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Calculation of Functionals Based on Large Dimension Matrixes in Maximal Likelihood Problems

Medvedev G.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2005

Vol. 10

95--105

The problem of the likelihood function calculation is examined AT parameter estimation of the stochastic process describing the change of interest rates in the financial market. Such a problem arises, when it is supposed that the process is not a usual diffusion process, but posesses continuous derivatives. In this case the increments of the proccess become correlated, and for the likelihood function evaluation it is necessary to invert a matrix of the high order equal to sample size. As it is known the calculation of reciprocal matrixes of the high order either is impossible or results in essential error of calculation. In this paper the way to avoid this difficulty is offered.

The No Arbitrage Conditions in the Segmented Markets

Medvedev G.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2003

Vol. 9

69--73

The present paper is the direct continuation of papers Medvedev (2001, 2002). In the financial market the term arbitrage refers to the possibility of making a trading gain with no chance of loss. The idea expressed by the no arbitrage condition consists that in the equilibrium market two portfolios of securities, which ensure identical payments, should have in each instant the identical price. Intuitively it is clear that such a definition of the price excludes the arbitrage. The arbitrage theory of market asset pricing is recently popular. It bases on the assumption that the financial market is arbitrage-free. To check the fulfillment of such assumption it is necessary to have some "no arbitrage" conditions. This explains the interest to derive such conditions.