Optimal Stopping and Utility in a Simple Modelof Unemployment Insurance

Risks

Leonid V. Bogachev¹  Jason S. Anquandah¹ 

[1] Department of Statistics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK;

关键词: insurance;    unemployment;    optimal stopping;    geometric Brownian motion;    martingale;    free boundary problem;    American call option;    utility;   

DOI  :  10.3390/risks7030094

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown