arXiv subjects

Leslaw Gajek

Publications and source records attributed to Leslaw Gajek.

2 recordsLinked to original sources

arXiv2015

On the martingale-fair index of return for investment funds

A concept of martingale-fair index of return, consistent with Arbitrage Free Pricing Theory, is introduced. An explicit formula for the average rate of return of a group of investment/pension funds in a discrete time stochastic model is derived and several properties of this index are shown. In particular, it is proven to be martingale-fair, i.e. be a martingale provided the prices of assets on the financial market form a vector martingale. The problem of merger of the funds is treated in detail.

q-fin.PM↗

arXiv2015

On the average rate of return in a continuous time stochastic model

In a discrete time stochastic model of a pension investment funds market Gajek and Kaluszka(2000a) have provided a definition of the average rate of return which satisfies a set of economic correctnes postulates. In this paper the average rate of return is defined for a continuous time stochastic model of the market. The prices of assets are modeled by the multidimensional geometrical Brownian motion. A martingale property of the average rate of return is proven.

math.PR↗