A new methodological framework for liability valuation affected by multi-period capital requirements

This paper conducts a comprehensive study on how multi-period capital requirements influence liability valuation and discuss the valuation problem under conditions of distributional uncertainty. We propose a new methodological framework for liability pricing that addresses scenarios where companies may avoid immediate bankruptcy despite insolvency, while also incorporating the impact of Ponzi dividends.The framework's theoretical consistency and operational mechanisms are rigorously examined. In particular, we analyze how changes in the risk-free interest rate affect the valuation results, drawing on principles from stochastic interest rate theory. For cases where risky asset prices follow geometric Brownian motion, we derive a closed-form pricing formula by iteratively solving the model's recursive valuation equations.Instead of assuming precise knowledge of future asset price distributions, we try to integrate distributional uncertainty into the model and adopt a distributionally robust optimization approach. By defining an ambiguity set based on moment constraints, we identify the worst-case distribution under a pessimistic decision-making paradigm. This methodology aligns with regulatory guidelines that prioritize cautious capital adequacy assessments.