Dimensions of Observable Support
retrieve_support.RdThis helper function returns the observable support of the lifetime and left-truncation random variables (e.g., Lautier et al., 2026).
Arguments
- Delta
A nonnegative integer denoting the period of time (in months) during which the ABS is marketed to prospective investors. It is after the trust closes to new loan originations but before its first reporting month.
- m
A positive integer representing the total number of months over which the underlying consumer auto loans are originated. This defines the length of the loan origination window before the trust closes.
- omega
A positive integer denoting the known, finite upper bound of a loan's lifetime (in months), which is nonrandom and observable from its amortization schedule at contract signing (for example, for a 72-month loan, we likely have \(\omega = 72\)).
- epsilon
A positive integer (default is
NULL) denoting the present time (the current calendar month age since the first loan was originated) of the data generation process for an active ABS pool. If \(\varepsilon < \omega + m\), then right-censoring is present because it indicates some active loans are still making ongoing payments and have not yet terminated (Lautier et al., 2023)
Value
A list with two integer vectors: X, the observable support
of the lifetime variable (from \(\Delta + 1\) to \(\xi\)), and
Y, the support of the left-truncation variable (from
\(\Delta + 1\) to \(\Delta + m\)).
Note
The observed support may not extend all the way to \(\omega\)
(omega). In that scenario, we set \(\omega\) to the age of the
oldest active loan in the ABS bond (corresponding to \(\xi \equiv
\min(\omega, \varepsilon - 1)\) in the notation used in Lautier et
al., 2023), with \(\varepsilon\) denoting the present time.
References
Lautier, J. P., Pozdnyakov, V., Yan, J. (2023). Pricing time-to-event contingent cash-flows: A discrete-time survival analysis approach. Insurance: Mathematics and Economics, 110, 53-71. https://doi.org/10.1016/j.insmatheco.2023.02.003
Lautier, J. P., Pozdnyakov, V., Yan, J. (2026). Estimating a discrete distribution subject to random left-truncation with an application to structured finance. Econometrics and Statistics, 37, 174-198. https://doi.org/10.1016/j.ecosta.2023.05.005