Envelope condition method with an application to default risk models

We develop an envelope condition method (ECM) for dynamic programming problems – a tractable alternative to expensive conventional value function iteration (VFI). ECM has two novel features: first, to reduce the cost of iteration on Bellman equation, ECM constructs policy functions using envelope conditions which are simpler to analyze numerically than first-order conditions. Second, to increase the accuracy of solutions, ECM solves for derivatives of value function jointly with value function itself. We complement ECM with other computational techniques that are suitable for high-dimensional problems, such as simulation-based grids, monomial integration rules and derivative-free solvers. The resulting value-iterative ECM method can accurately solve models with at least up to 20 state variables and can successfully compete in accuracy and speed with state-of-the-art Euler equation methods. We also use ECM to solve a challenging default risk model with a kink in value and policy functions.     

Sequential optimization three-way decision model with information gain for credit default risk evaluation

To categorize credit applications into defaulters or non-defaulters, most credit evaluation models have employed binary classification methods based on default probabilities. However, while some loan applications can be directly accepted or rejected, there are others on which immediate accurate credit status decisions cannot be made using existing information. To resolve these issues, this study developed an optimized sequential three-way decision model. First, an information gain objective function was built for the three-way decision, after which a genetic algorithm (GA) was applied to determine the optimal decision thresholds. Then, appropriate accept or reject decisions for some applicants were made using basic credit information, with the remaining applicants, whose credit status was difficult to determine, being divided into a boundary region (BND). Supplementary information was then added to reevaluate the credit applicants in the BND, and a sequential optimization process was employed to ensure more accurate predictions. Therefore, the model’s predictive abilities were improved and the information acquisition costs controlled. The empirical results demonstrated that the proposed model was able to outperform other benchmarking credit models based on performance indicators.