Comparing Local Risks by Acceptance and Rejection

15 Pages Posted: 13 Mar 2012

See all articles by Amnon Schreiber

Amnon Schreiber

Hebrew University of Jerusalem; Bar-Ilan University - Department of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: March 12, 2012

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.

Keywords: riskiness, risk, acceptance dominance, measure of riskiness, securities

Suggested Citation

Schreiber, Amnon, Comparing Local Risks by Acceptance and Rejection (March 12, 2012). Available at SSRN: https://ssrn.com/abstract=2020199 or http://dx.doi.org/10.2139/ssrn.2020199

Amnon Schreiber (Contact Author)

Hebrew University of Jerusalem ( email )

Mount Scopus
Jerusalem, Jerusalem 91905
Israel

Bar-Ilan University - Department of Economics ( email )

Ramat-Gan, 52900
Israel

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