Stability properties of Haezendonck-Goovaerts premium principles

2019/09/24 by Gao, Niushan, Munari, Cosimo, Xanthos, Foivos · 1 citation
#FOS: Economics and business #Mathematical Finance (q-fin.MF) #Risk Management (q-fin.RM)

paper · doi:10.48550/arxiv.1909.10735

Abstract

We investigate a variety of stability properties of Haezendonck-Goovaerts premium principles on their natural domain, namely Orlicz spaces. We show that such principles always satisfy the Fatou property. This allows to establish a tractable dual representation without imposing any condition on the reference Orlicz function. In addition, we show that Haezendonck-Goovaerts principles satisfy the stronger Lebesgue property if and only if the reference Orlicz function fulfills the so-called Δ₂ condition. We also discuss (semi)continuity properties with respect to Φ-weak convergence of probability measures. In particular, we show that Haezendonck-Goovaerts principles, restricted to the corresponding Young class, are always lower semicontinuous with respect to the Φ-weak convergence.

Cited by

• Orlicz-Lorentz premia and distortion Haezendonck-Goovaerts risk measures

Related

• Fatou Property, representations, and extensions of law-invariant risk\n measures on general Orlicz spaces
• Separability vs. robustness of Orlicz spaces: financial and economic perspectives
• On the C-property and w^*-representations of risk measures
• Equivalence between tails, Grand Lebesgue Spaces and Orlicz norms for random variables without Cramer's condition
• Convex functions on dual Orlicz spaces