Fair allocation of capital growth

Karl Michael Ortmann ()
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Karl Michael Ortmann: Beuth University of Applied Sciences Berlin

Operational Research, 2016, vol. 16, issue 2, No 2, 196 pages

Abstract: Abstract Financial investments are usually modelled and analysed by assuming exponential growth. For consistency purposes, we model savings products and interest-bearing securities as multiplicative cooperative games with transferable utility. The agents of these games are time periods and we are interested in a fair decomposition of the total growth factor. Notably, any financial transaction is governed by a suitable capital accumulation function. Therefore, we transfer this concept to cooperative game theory by establishing the notion of an accumulation function for coalitions. This property relates to a no-arbitrage principle and implies the law of one price. In particular, we show that the multiplicative variant of the Shapley value is the only efficient value that is associated with the concept of an accumulation function for coalitions. Using similarity conclusions, the original Shapley value can be uniquely characterised by applying efficiency and an additive accumulation function. Furthermore, the accumulation function coincides with the potential of the Shapley value.

Keywords: Shapley value; Potential; Accumulation function; Arbitrage (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s12351-015-0191-z

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