A time-dependent stopping problem with application to live organ transplantation

Extract

Offers become available from time to time. The offers constitute a sequence of i.i.d. positive random variables. Upon arrival of an offer a decision is taken whether to accept it or not. When an offer is accepted the process terminates. Otherwise, the offer is lost and the process continues until the next arrival or until a moment where it terminates by itself. The probability of self-termination depends on the age of the underlying process.