Jincheng Zhang
This paper investigates the concept of "commitment lifetime" within the context of decentralized finance (DeFi) protocols, specifically focusing on the variability in the duration a user's commitment to a collateralized asset remains valid. The commitment lifetime, denoted as *LC(P)*, is defined as the difference between the release time and the birth time of the commitment, where *trelease* and *tbirth* represent the respective timestamps. The core objective is to analyze the probability distribution of commitment lifetimes, denoted as *P(LC > t)*, for different algorithmic approaches used in managing collateralized positions. We demonstrate that despite potentially differing underlying mechanisms, various DeFi protocols can arrive at identical conclusions regarding commitment lifetimes. This highlights the importance of understanding the mathematical representation of commitment lifetime distributions, which we term the "commitment lifetime distribution." This analysis provides a foundational understanding for risk management and parameter optimization within DeFi systems.