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Abstract

We extend the celebrated Rothschild and Stiglitz (1970) definition of Mean Preserving Spreads to scalar diffusion processes. We provide sufficient conditions under which a family of diffusion processes satisfies the dynamic counterparts to the famous Rothschild and Stiglitz integral conditions. We prove that the only Brownian bridge with non-constant drift that displays the Dynamic Mean-Preserving Spread (DMPS) property is given by the ballistic super-diffusive process. We illustrate our results in the context of the cannonical examples of investment under uncertainty and option pricing.

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