Facoltà di scienze economiche

Asset pricing with no exogenous probability measure

Cassese, Gianluca

In: Mathematical finance, 2008, vol. 18, no. 1, p. 23-54

In this paper we propose a model of financial markets in which agents have limited ability to trade and no probability is given from the outset. In the absence of arbitrage opportunities, assets are priced according to a probability measure that lacks countable additivity. Despite finite additivity, we obtain an explicit representation of the expected value with respect to the pricing measure,... Plus

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    Summary
    In this paper we propose a model of financial markets in which agents have limited ability to trade and no probability is given from the outset. In the absence of arbitrage opportunities, assets are priced according to a probability measure that lacks countable additivity. Despite finite additivity, we obtain an explicit representation of the expected value with respect to the pricing measure, based on some new results on finitely additive measures. From this representation we derive an exact decomposition of the rsik premiu as the sum of the correlation of returns with the market price of risk and an additional term, the purely nitely additive premium, related to the jumps of the return process. We also discuss the implications of the absence of free lunches.