Solving HACT models with bankruptcy choice
在连续时间异质性主体框架中引入破产选择，提出仅用价值匹配条件高效求解，并推荐线性互补问题求解器，适用于控制变量依赖价值函数斜率的场景。
We introduce bankruptcy choice to the heterogeneous agent in continuous time (HACT) framework developed in Achdou et al. (2022). We demonstrate that real-options-like problems such as the decision to declare bankruptcy can be efficiently solved using the “value-matching” condition only (unlike alternative methods that require both value matching and “smooth pasting”). Moreover, we show that under certain conditions, smooth-pasting may not hold. Given this, we recommend (and demonstrate the use of) linear complementarity problem (LCP) solvers for real-option like problems, especially in settings where control variables depend on the slope of the value function. We show that this approach is more flexible and computationally efficient than other popular solution methods. In particular, it is less prone to errors in settings that have corner solutions. • This note introduces bankruptcy choice to the heterogeneous agent in continuous time (HACT) framework. • We show that in certain settings we cannot rely on the smooth pasting condition to solve models with bankruptcy choice. • We suggest a solution approach that is more flexible and computationally efficient than other alternatives used in HACT models. • Our approach is less prone to errors with problems that have corner solutions.