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Open AccessFeature PaperArticle

Optimal Stopping and Utility in a Simple Modelof Unemployment Insurance

Department of Statistics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
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Risks 2019, 7(3), 94; https://doi.org/10.3390/risks7030094
Received: 30 January 2019 / Revised: 15 August 2019 / Accepted: 18 August 2019 / Published: 1 September 2019
(This article belongs to the Special Issue Applications of Stochastic Optimal Control to Economics and Finance)
Managing unemployment is one of the key issues in social policies. Unemployment insurance schemes are designed to cushion the financial and morale blow of loss of job but also to encourage the unemployed to seek new jobs more proactively due to the continuous reduction of benefit payments. In the present paper, a simple model of unemployment insurance is proposed with a focus on optimality of the individual’s entry to the scheme. The corresponding optimal stopping problem is solved, and its similarity and differences with the perpetual American call option are discussed. Beyond a purely financial point of view, we argue that in the actuarial context the optimal decisions should take into account other possible preferences through a suitable utility function. Some examples in this direction are worked out. View Full-Text
Keywords: insurance; unemployment; optimal stopping; geometric Brownian motion; martingale; free boundary problem; American call option; utility insurance; unemployment; optimal stopping; geometric Brownian motion; martingale; free boundary problem; American call option; utility
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Anquandah, J.S.; Bogachev, L.V. Optimal Stopping and Utility in a Simple Modelof Unemployment Insurance. Risks 2019, 7, 94.

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