Optimal Effort on Self-Insurance-Cum-Protection: A New Analysis Using Yaari’s Dual Theory

People take different measures to control risks. The measures that can simultaneously reduce loss probability and loss size are called self-insurance-cum-protection. This paper studies self-insurance-cum-protection using Yaari’s dual theory. We analyze the comparative statics of increased risk avers...

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Autores principales:	Wing Yan Lee, Derrick W. H. Fung
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	self-insurance-cum-protection dual theory risk aversion market insurance Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/f85c6809ae5548f5ba4717bd97da9816
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spelling	oai:doaj.org-article:f85c6809ae5548f5ba4717bd97da98162021-11-25T18:16:37ZOptimal Effort on Self-Insurance-Cum-Protection: A New Analysis Using Yaari’s Dual Theory10.3390/math92228532227-7390https://doaj.org/article/f85c6809ae5548f5ba4717bd97da98162021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2853https://doaj.org/toc/2227-7390People take different measures to control risks. The measures that can simultaneously reduce loss probability and loss size are called self-insurance-cum-protection. This paper studies self-insurance-cum-protection using Yaari’s dual theory. We analyze the comparative statics of increased risk aversion. Two different sufficient conditions are found in the two-state model, from which an increase in the level of risk aversion will lead to an increase in the level of self-insurance-cum-protection. The first condition is a new result under Yaari’s dual theory and its implication is that the more risk-averse individual is willing to exert greater effort on self-insurance-cum-protection if the probability of loss can be reduced to very small by a less risk-averse individual with optimal effort. The second condition depends on the forms of the self-insurance-cum protection cost and the loss. This condition is the same as that obtained under expected utility in existing literature. Our study therefore assures the robustness this result. We also study comparative statics in the continuous model and find out that the results are analogous to that in the two-state model. In addition, we consider how the availability of market insurance affects the self-insurance-cum-protection level. When the probability of loss is small, the self-insurance-cum-protection and market insurance are substitutes. This means when market insurance is available, people tend to exert less effort on self-insurance-cum-protection.Wing Yan LeeDerrick W. H. FungMDPI AGarticleself-insurance-cum-protectiondual theoryrisk aversionmarket insuranceMathematicsQA1-939ENMathematics, Vol 9, Iss 2853, p 2853 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	self-insurance-cum-protection dual theory risk aversion market insurance Mathematics QA1-939
spellingShingle	self-insurance-cum-protection dual theory risk aversion market insurance Mathematics QA1-939 Wing Yan Lee Derrick W. H. Fung Optimal Effort on Self-Insurance-Cum-Protection: A New Analysis Using Yaari’s Dual Theory
description	People take different measures to control risks. The measures that can simultaneously reduce loss probability and loss size are called self-insurance-cum-protection. This paper studies self-insurance-cum-protection using Yaari’s dual theory. We analyze the comparative statics of increased risk aversion. Two different sufficient conditions are found in the two-state model, from which an increase in the level of risk aversion will lead to an increase in the level of self-insurance-cum-protection. The first condition is a new result under Yaari’s dual theory and its implication is that the more risk-averse individual is willing to exert greater effort on self-insurance-cum-protection if the probability of loss can be reduced to very small by a less risk-averse individual with optimal effort. The second condition depends on the forms of the self-insurance-cum protection cost and the loss. This condition is the same as that obtained under expected utility in existing literature. Our study therefore assures the robustness this result. We also study comparative statics in the continuous model and find out that the results are analogous to that in the two-state model. In addition, we consider how the availability of market insurance affects the self-insurance-cum-protection level. When the probability of loss is small, the self-insurance-cum-protection and market insurance are substitutes. This means when market insurance is available, people tend to exert less effort on self-insurance-cum-protection.
format	article
author	Wing Yan Lee Derrick W. H. Fung
author_facet	Wing Yan Lee Derrick W. H. Fung
author_sort	Wing Yan Lee
title	Optimal Effort on Self-Insurance-Cum-Protection: A New Analysis Using Yaari’s Dual Theory
title_short	Optimal Effort on Self-Insurance-Cum-Protection: A New Analysis Using Yaari’s Dual Theory
title_full	Optimal Effort on Self-Insurance-Cum-Protection: A New Analysis Using Yaari’s Dual Theory
title_fullStr	Optimal Effort on Self-Insurance-Cum-Protection: A New Analysis Using Yaari’s Dual Theory
title_full_unstemmed	Optimal Effort on Self-Insurance-Cum-Protection: A New Analysis Using Yaari’s Dual Theory
title_sort	optimal effort on self-insurance-cum-protection: a new analysis using yaari’s dual theory
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/f85c6809ae5548f5ba4717bd97da9816
work_keys_str_mv	AT wingyanlee optimaleffortonselfinsurancecumprotectionanewanalysisusingyaarisdualtheory AT derrickwhfung optimaleffortonselfinsurancecumprotectionanewanalysisusingyaarisdualtheory
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Optimal Effort on Self-Insurance-Cum-Protection: A New Analysis Using Yaari’s Dual Theory

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