A Birandom Job Search Problem with Risk Tolerance

This paper considers a novel class of birandom job search problem, in which the job offers are sampled by the job searcher from a finite job set with equivalent probability and their wages are characterized as independent but maybe not identically nonnegative random variables. The job searcher knows the job offer's wage distribution when he samples the job offer. Since the offered wage is a random variable and the reservation wage is a deterministic number, it is meaningless to make comparison directly. In order to rank the random wage and the reservation wage and provide decision support, a risk tolerance criterion is designed, and the job searcher then accepts or rejects the sampled job offer depending on whether the risk tolerance criterion is met or not. Since the offered wages are random variables and the search process is random, it's impossible to obtain the job searcher's real return; in this case, its expected value can be calculated via birandom theory. Simultaneously, some propositions on the expected return as well as the average search times are also studied which may provide some valuable suggestions to the job searcher. Numerical examples are given to illustrate the decision process of the risk tolerance-based birandom job search problem