This paper extends the concept of stochastic dominance to dynamic environments. Our primary result is a characterization of dominance orders between stochastic payoff processes, determined by unanimity among groups of discounted expected utility maximizers. We investigate the implications of this characterization for first-order dynamic stochastic dominance when payoffs follow standard diffusion processes. Additionally, we introduce a measure to quantify the intensity of dominance between payoff processes, which we then use to derive robust bounds on asset price differentials.
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