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Least-Squares Prices of Coin-Flipping Games

Yukio Hirashita

Abstract


What are the prices of random variables? We assert that the prices are not necessarily their (arithmetic, geometric, discounted) means. In this paper, we first present the geometric price of a single coin-flipping game. Second, we define the least-squares prices in the convex cone of coin-flipping games, which are proved to be minimal, positive linear, and arbitrage-free. These least-squares prices depend both on a set of games that is available for simultaneous investment and on a risk-free interest rate.

Keywords


Pricing, Growth rate, Convex cone.

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