Almost expectation and excess dependence notions

This paper weakens the expectation dependence concept due to Wright (Theory Decis 22:111-124, 1987) and its higher-order extensions proposed by Li (J Econ Theory 146:372-391, 2011) to conform with the preferences generating the almost stochastic dominance rules introduced in Leshno and Levy (Manag Sci 48:1074-1085, 2002). A new dependence concept, called excess dependence is introduced and studied in addition to expectation dependence. This new concept coincides with expectation dependence at first-degree but provides distinct higher-order extensions. Three applications, to portfolio diversification, to the determination of the sign of the equity premium in the consumption-based CAPM, and to optimal investment in the presence of a background risk, illustrate the usefulness of the approach proposed in the present paper.