Abstract
It is said that risky asset h acceptance dominates risky asset k if any decision maker who rejects the investment in h rejects also the investment in k. As Hart (2011) shows, acceptance dominance is an incomplete order on an ordinary set of gambles. We extend the definition of acceptance dominance order to risky assets whose values follow random processes. We call the risk that arises from investing in such assets, with a short investment time horizon, local risk. We show that for small investment time horizons, the acceptance dominance order is a complete order that can be represented by an index of local risk. Moreover, we show that the measures of riskiness proposed by Aumann & Serrano (2008), Foster & Hart (2009), and Schreiber (2011) all coincide with our index. We use the differential calculus as an analytical tool to present our results.
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