[2603.26309] Semi-structured multi-state delinquency model for mortgage default

Statistics > Applications arXiv:2603.26309 (stat) [Submitted on 27 Mar 2026] Title:Semi-structured multi-state delinquency model for mortgage default Authors:Victor Medina-Olivares, Wangzhen Xia, Stefan Lessmann, Nadja Klein View a PDF of the paper titled Semi-structured multi-state delinquency model for mortgage default, by Victor Medina-Olivares and Wangzhen Xia and Stefan Lessmann and Nadja Klein View PDF HTML (experimental) Abstract:We propose a semi-structured discrete-time multi-state model to analyse mortgage delinquency transitions. This model combines an easy-to-understand structured additive predictor, which includes linear effects and smooth functions of time and covariates, with a flexible neural network component that captures complex nonlinearities and higher-order interactions. To ensure identifiability when covariates are present in both components, we orthogonalise the unstructured part relative to the structured design. For discrete-time competing transitions, we derive exact transformations that map binary logistic models to valid competing transition probabilities, avoiding the need for continuous-time approximations. In simulations, our framework effectively recovers structured baseline and covariate effects while using the neural component to detect interaction patterns. We demonstrate the method using the Freddie Mac Single-Family Loan-Level Dataset, employing an out-of-time test design. Compared with a structured generalised additive benchmark, the ...