A benchmark approach to investing and pricing

World Scientific Publishing
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The Kelly Capital Growth Investment Criterion: Theory and Practice, 2011, 1, pp. 409 - 426
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This paper introduces a general market modeling framework, the benchmark appma.chl which assumes the existence of the nume!'raire portfolio. This is the strictly positive portfolio that when used as benchmMk makes all benchmarked non-negati.ve portfolios sllperma.rtinga!es, that is intuitively speaking downward trending or trendless. It can be shQ'Wn to equal the Kelly portfolio, which tna.-"jmiz. es expected logarithmk utility. In several Wa.ys, the KeUy or numeraire portfolio is the "bestll performing portfolio and cannot be outperformed systematically by any other non-negative portfolio. Its use in pricing as nttmeroire leads directly to the real world pricing formula) which employs the real world probability when calculating conditional expectations. In a large regular financial market, the Kelly portfolio is shawn to be approxima.ted by well·divcnrified portfolios.
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