UPA Perpustakaan Universitas Jember

The growth of relative wealth and the Kelly criterion

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We propose an evolutionary framework for optimal portfolio growth theory
in which investors subject to environmental pressures allocate their wealth between
two assets. By considering both absolute wealth and relative wealth between investors,
we show that different investor behaviors survive in different environments. When
investors maximize their relative wealth, the Kelly criterion is optimal only under
certain conditions, which are identified. The initial relative wealth plays a critical role
in determining the deviation of optimal behavior from the Kelly criterion regardless
of whether the investor is myopic across a single time period or maximizing wealth
over an infinite horizon. We relate these results to population genetics, and discuss
testable consequences of these findings using experimental evolution.

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