Optimal Insurance Contracts Under Distortion Risk Measures With Ambiguity Aversion

Abstract

This paper presents analytical representations for an optimal insurance contract under distortion risk measure and in the presence of model uncertainty. We incorporate ambiguity aversion and distortion risk measure through the model of Robert and Therond [(2014) ASTIN Bulletin: The Journal of the IAA, 44(2), 277–302.] as per the framework of Klibanoff et al. [(2005) A smooth model of decision making under ambiguity. Econometrica, 73(6), 1849–1892.]. Explicit optimal insurance indemnity functions are derived when the decision maker (DM) applies Value-at-Risk as risk measure and is ambiguous about the loss distribution. Our results show that: (1) under model uncertainty, ambiguity aversion results in a distorted probability distribution over the set of possible models with a bias in favor of the model which yields a larger risk; (2) a more ambiguity-averse DM would demand more insurance coverage; (3) for a given budget, uncertainties about the loss distribution result in higher risk level for the DM.

Worst-case moments under partial ambiguity

“…Often being a critical issue in insurance practice, model uncertainty has received increasing attention in the insurance literature. The following works, among others, have investigated or touched this issue in various insurance contexts: Cairns (2000), Chen and Su (2009), Peters et al (2009), Zhao and Zhu (2011) , Landsman and Tsanakas (2012), Robert and Therond (2014), Liu and Wang (2017), Fujii et al (2017), and Jiang et al (2020). More applications to practical problems in insurance have been proposed during recent years but are still sporadic; see Wozabal (2014), Pflug et al (2017), Lam and Mottet (2017), Asimit et al (2017Asimit et al ( , 2019, Ghossoub (2019aGhossoub ( , 2019b, , Pflug (2019), andBirghila et al (2020), among others.…”

“…(2017), and Jiang et al . (2020). More applications to practical problems in insurance have been proposed during recent years but are still sporadic; see Wozabal (2014), Pflug et al .…”

Culture and the demand for non‐life insurance: Empirical evidences from middle‐income and high‐income economies*

“…In a related work, Jiang et al. (2020) derived the explicit optimal insurance indemnity functions when the decision maker applies value‐at‐risk as risk measure and found that a more ambiguity‐averse decision maker would demand more insurance coverage.…”

A Marginal Indemnity Function Approach to Optimal Reinsurance under the Vajda Condition

“…More such examples of optimal reinsurance that can be written of the form of (2.4) can be found in Assa (2015) , Boonen, Tan, & Zhuang (2016) , Asimit & Boonen (2018) , Lo & Tang (2019) . In the presence of model ambiguity, we refer the interested readers to Hansen & Sargent (2011) for many basic and advanced techniques in robust decision making, and Birghila & Pflug (2019) , Birghila, Boonen, &Ghossoub (2020) , andJiang, Escobar-Anel, &Ren (2020) for some recent advances on robust insurance contracting. In the next subsection, we present the main problem to be addressed in this paper.…”