Fractional-Degree Expectation Dependence

Abstract

We develop a fractional-degree expectation dependence which is the generalization of the first-degree and second-degree expectation dependence. The motivation for introducing such a dependence notion is to conform with the preferences of decision makers who are mostly risk averse but would be risk seeking at some wealth levels. We investigate some tractable equivalent properties for this new dependence notion, and explore its properties, including the invariance under increasing and concave transformations, and the invariance under convolution. We also extend our results to a combined fractional-degree expectation dependence notion including $\varepsilon $-almost first-degree expectation dependence. Two applications on portfolio diversification problem and optimal investment in the presence of a background risk illustrate the usefulness of the approaches proposed in the present paper.

Keywords

Expectation dependence / Incomplete risk aversion / Confined correlation aversion / Optimal investment

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Funding

National Natural Science Foundation of China(11701518)

Natural Science Foundation of Zhejiang Province(LQ17A010011))

Zhejiang SCI-TECH university foundation(16062097- Y)