Journal article
Arrow's Theorem of the Deductible with Heterogeneous Beliefs
North American actuarial journal, Vol.21(1), pp.15-35
01/02/2017
DOI: 10.1080/10920277.2016.1192477
Abstract
In Arrow's classical problem of demand for insurance indemnity schedules, it is well-known that the optimal insurance indemnification for an insurance buyer-or decision maker (DM)-is a deductible contract when the insurer is a risk-neutral Expected-Utility (EU) maximizer and when the DM is a risk-averse EU maximizer. In Arrow's framework, however, both parties share the same probabilistic beliefs about the realizations of the underlying insurable loss. This article reexamines Arrow's problem in a setting where the DM and the insurer have different subjective beliefs. Under a requirement of compatibility between the insurer's and the DM's subjective beliefs, we show the existence and monotonicity of optimal indemnity schedules for the DM. The belief compatibility condition is shown to be a weakening of the assumption of a monotone likelihood ratio. In the latter case, we show that the optimal indemnity schedule is a variable deductible schedule, with a state-contingent deductible that depends on the state of the world only through the likelihood ratio. Arrow's classical result is then obtained as a special case.
Details
- Title: Subtitle
- Arrow's Theorem of the Deductible with Heterogeneous Beliefs
- Creators
- Mario Ghossoub - Imperial College London
- Resource Type
- Journal article
- Publication Details
- North American actuarial journal, Vol.21(1), pp.15-35
- DOI
- 10.1080/10920277.2016.1192477
- ISSN
- 1092-0277
- eISSN
- 2325-0453
- Publisher
- Taylor & Francis
- Number of pages
- 21
- Grant note
- Waterloo Research Institute in Insurance, Securities and Quantitative Finance Natural Sciences and Engineering Research Council of Canada; Natural Sciences and Engineering Research Council of Canada (NSERC); CGIAR Society of Actuaries Social Sciences and Humanities Research Council of Canada; Social Sciences & Humanities Research Council of Canada (SSHRC)
- Language
- English
- Date published
- 01/02/2017
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9985179681002771
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