Abstract We describe a mathematical model for the consumer debt repayment by a representative rational household. The household’s objective is to maximize a utility functional comprising two components: the first represents utility derived during the debt repayment period, and the second captures the expected utility from economic preferences after the loan is fully repaid. The model is formalized as an optimal control problem featuring a non-compact control set and an endogenous time horizon. We provide the analysis of the post-repayment utility functional and examine how the resulting expected profit of a commercial bank depends on the household’s chosen repayment strategy.
Шананин et al. (Sun,) studied this question.