# The average risk sharing problem under risk measure and expected utility theory

*Tiantian Mao*,
*Jiuyun Hu* and
*Haiyan Liu*

*Insurance: Mathematics and Economics*, 2018, vol. 83, issue C, 170-179

**Abstract:**
In this paper, we investigate an average risk sharing problem, in which the optimal objective function is called an average-inf-convolution. We study the properties of the average-inf-convolution for a general risk measure, and obtain the explicit form of the average-inf-convolution. We also analyze the average risk sharing problems in the classic utility models in behavioral economics. Explicit forms of the average-inf-convolutions are obtained in the expected utility model and in the utility-based shortfall model, respectively. In the rank-dependent expected utility (RDEU) model, we give a lower bound of the average-inf-convolution for the RDEU-based shortfall.

**Keywords:** Risk sharing; Average-inf-convolution; Expected utility; Convex risk measure; Utility-based shortfall (search for similar items in EconPapers)

**Date:** 2018

**References:** View references in EconPapers View complete reference list from CitEc

**Citations** Track citations by RSS feed

**Downloads:** (external link)

http://www.sciencedirect.com/science/article/pii/S0167668717306194

Full text for ScienceDirect subscribers only

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:eee:insuma:v:83:y:2018:i:c:p:170-179

Access Statistics for this article

Insurance: Mathematics and Economics is currently edited by *R. Kaas*, *Hansjoerg Albrecher*, *M. J. Goovaerts* and *E. S. W. Shiu*

More articles in Insurance: Mathematics and Economics from Elsevier

Bibliographic data for series maintained by Dana Niculescu ().