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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.

preprint2015arXivOpen access
Leslaw GajekMarek Kaluszka
math.PRq-fin.PM
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Leslaw GajekMarek Kaluszka

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