  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
pro-actively 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.
