Options
Analysis and optimization of the creditworthiness threshold under different bivariate distributions
Date Issued
2025
Publisher
World Scientific Pub Co Pte Ltd
ISSN
0217-5959
1793-7019
Citation
Asia-Pacific Journal of Operational Research, 2025.
Type
Peer Reviewed Journal Article
Abstract
Classifying the creditworthiness of credit applicants is an important decision-making issue for both practitioners and researchers and assists practitioners in the financial sector to determine whether to accept or reject a credit application. However, it is difficult to find real applications that use bivariate distribution models with the continuous optimization method because of the necessity to identify the distribution of credit applicants. To bridge the gap in the literature, in this paper, we develop the theory of the creditworthiness threshold in terms of the cost and revenue payoff matrix formulation and introduce an optimization method to obtain an approximation for the credit applicants’ distribution. Based on maximizing the expected profit by taking the difference between two identical and independent distributions, we introduce two bivariate models in this paper for classifying the Good and Bad groups: the Inverse Gaussian-Inverse Gaussian model and the Laplace–Laplace model. In this paper, we propose an approach using the continuous optimization method and our proposed approach to obtain the threshold value is easy to use. Moreover, this threshold value is proven to be the optimal value of the profit function and is offered in terms of a closed-form expression, both characteristics that benefit practitioners, allowing them to get a simple but reliable optimal threshold value to support decision-making for a credit application. To demonstrate the applicability of the theory we developed in this paper, we first use six different cases with consistent means and proportions for the Good and Bad populations to create a synthetic dataset for all our numerical simulation testing. In addition, we provide an approach for analyzing the problem and obtaining the solution of an optimal creditworthiness threshold value with a closed-form expression. Moreover, we contribute to the literature by providing proof of how each bivariate distribution model can be used for identifying a local or a global maximum threshold value based on the choices of parameters and a constrained interval. We provide numerical computations and related interpretations based on sensitivity analysis of the results, for example, the four values of a two-by-two cost and revenue payoff matrix, to justify our theoretical findings. We then evaluate the performance of our proposed model by using real-life data from South German Credit. Both synthetic and real-life datasets are used in this paper to present a detailed theoretical, analytical, and empirical comparison of our proposed findings and demonstrate their comparative utility, efficiency, and accuracy, focusing primarily on several case studies using sensitivity analysis.
Loading...
Availability at HKSYU Library
