2023 Australasian Actuarial Education and Research Symposium

Zheng Xu

Australian National University

The optimal repayment structure of agricultural loans

This is joint work with Marcos Escobar-Anel, Gaurav Khemka, Timothy Higgins

We investigate the optimal asset allocation and repayment strategy of an agricultural loan under a condition of guaranteed repayment. Using dynamic programming, we solve an expected utility-maximization problem for 'net' consumption and terminal wealth. We demonstrate, for a wide family of income structures, that the existence of the loan and the corresponding repayment would not affect the farmer's optimal asset allocation strategy under a power utility framework because the farmer would invest the outstanding loan amount in a risk-free way to guarantee that the loan would be fully repaid at the end. We use the results of this analytical solution to explore the more interesting question of the impact on farmers' 'nominal' consumption and terminal wealth numerically, noting that the nominal problem does not have a closed-form solution. In the numerical study, we explore various forms of time-based (deterministic) and contingent (stochastic) repayment structures. The results show that the deterministic repayment structures outperform the stochastic ones. Furthermore, the numerical results reveal a convenient structure of the optimal repayment for the nominal problem.