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Zonoids induced by Gauss measure with an application to risk aversion

Suppose E is a real, separable Banach space and for each x ∈ E denote by co{0,(1, x)} the line segment joining the two points 0 and (1, x) in R × E. The aim of this paper is to discuss the strong law of large numbers and the central limit theorem for the random line segment co{0,(1, a + X)} when X is a centred Gaussian random vector in E and a ∈ E. Finally, an application to mathematical finance is given.