Department of

# Mathematics

Seminar Calendar
for events the day of Friday, January 23, 2015.

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events for the
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Questions regarding events or the calendar should be directed to Tori Corkery.
    December 2014           January 2015          February 2015
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1  2  3  4  5  6                1  2  3    1  2  3  4  5  6  7
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Friday, January 23, 2015

4:00 pm in 245 Altgeld Hall,Friday, January 23, 2015

#### Optimal Insurance with Heterogeneous Beliefs, and Some Extensions

###### Mario Ghossoub (Imperial College London)

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, the two parties share the same probabilistic beliefs about the realizations of the insurable loss. In this talk, we re-examine 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 an optimal indemnity schedule. We also fully characterize the class of optimal indemnity schedules that are non-decreasing in the loss, in terms of their distribution under the DM’s probability measure. Arrow’s classical result is then obtained as a special case of our main result. The belief compatibility condition is shown to be a weakening of the assumption of a Monotone Likelihood Ratio (MLR). Finally, we show that in the MLR case the optimal indemnity schedule is a state-contingent deductible contract. Time permitting, we examine some extensions to the case of ambiguous beliefs and more general premium principles.