A Benchmark Approach to Investing and Pricing

Eckhard Platen ()

Chapter 28 in The Kelly Capital Growth Investment Criterion:Theory and Practice, 2011, pp 409-426 from World Scientific Publishing Co. Pte. Ltd.

Abstract: This paper introduces a general market modeling framework, the benchmark approach, which assumes the existence of the numéraire portfolio. This is the strictly positive portfolio that when used as benchmark makes all benchmarked non-negative portfolios supermartingales, that is intuitively speaking downward trending or trendless. It can be shown to equal the Kelly portfolio, which maximizes expected logarithmic utility. In several ways, the Kelly or numéraire portfolio is the “best” performing portfolio and cannot be outperformed systematically by any other non-negative portfolio. Its use in pricing as numéraire 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 shown to be approximated by well-diversified portfolios.

Keywords: Kelly Criterion; Dynamic Investment Analysis; Capital Growth Theory; Sports Betting; Hedge Fund Strategies; Speculative Investing; Fortune 's Formula (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (14)

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Working Paper: A Benchmark Approach to Investing and Pricing (2009)
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