A note on the family of extremality stochastic orders

María Concepción López-Díaz and Miguel López-Díaz

Insurance: Mathematics and Economics, 2013, vol. 53, issue 1, 230-236

Abstract: The family of extremality stochastic orders was introduced in Laniado et al. (2012) (Portfolio selection through an extremality stochastic order. Insurance: Mathematics and Economics 51, 1–9), as an extension of the upper and lower orthant orders, having important applications in the research of optimal allocations of wealth among risks in single period portfolio problems. In this paper we analyze some properties of such a family of stochastic orders, namely we prove that any extremality stochastic order is generated by a partial order on the Euclidean space and the class of upper quadrant sets of the partial order, showing that all the extremality orders are order-isomorphic. The above analysis will lead to the determination of the maximal generator of each extremality order by means of the maximal generator of the upper orthant order. Moreover we introduce a new family of stochastic orders which arises from the previous construction.

Keywords: Extremality order; Maximal generator; Order-isomorphism; Order-preserving mapping; Partial order (search for similar items in EconPapers)
JEL-codes: C02 (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:53:y:2013:i:1:p:230-236

DOI: 10.1016/j.insmatheco.2013.04.009

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