Optimal Stopping for Actuarial Use: A Study on Unemployment Insurance Schemes

Managing unemployment is one of the key issues in social policies. Unemployment insurance schemes are designed not only to cushion against the severe blow to finance and morale caused by the loss of job but also to encourage the unemployed to seek new jobs more proactively due to the continuous reduction of benefit payments. This thesis is concerned with the entry time into unemployment insurance schemes. First, a simple model of unemployment insurance is proposed with a focus on optimality of the individual's entry into 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. Second, we expand the UI model by making the parameters time dependent. This causes obvious complications to the model and gives rise to an optimal stopping problem which involves the computation of a time dependent boundary. An exact computational formula for this time dependent optimal boundary is unknown. Nevertheless, some numerical approaches are proposed to approximate the optimal boundary. Third, we focus on the analysis and modelling the labour force data from the Office for National Statistics (ONS) in UK. The labour force data is used because it consistently captures in details the estimates of the number of individuals employed, unemployed and inactive in UK, which are key features needed to compute the unemployment and reemployment rates in our UI scheme. Additionally, aside the aforementioned key features, the data also details the movement of individuals between employment, unemployment, and inactivity. Hence enabling us to understand and interpret the changes in the level of the labour market per quarter. To make our UI model more realistic, we explore a variety of multi-state models and lake models using the data and give highlights of the approaches and the results. Finally, we summarise the results and indicate a few directives that can be further explored.