Abstract
We examine the optimal timing for climate adaptation investments as a continuous-time optimal stopping problem. Physical climate risk produces heavy- tailed loss distributions whose extremes grow with climate uncertainty; adaptation is an irreversible expense that provides a permanent reduction in those losses. We incorporate this structure within the Climate Capital Option Theory (CCOT) framework, which models adaptation as a protective put option on a stochastic climate-loss process. The investment decision reduces to: exercise the option the first time a climate- or financial-stress indicator exceeds an endogenous threshold τ*. We derive τ* explicitly, analyse its comparative-static properties concerning climate uncertainty, the regulatory capital cost coefficient η, and the adaptation cost I0, and demonstrate that τ* is non-decreasing with the variance of the loss process. A formal sensitivity analysis reveals that increasing climate uncertainty — understood as a mean-preserving spread on the loss distribution — decreases the optimal threshold, thereby making early investment unequivocally optimal. A numerical example involving a multi-hazard manufacturing asset in the Philippines supports the theory: the tail-risk capital benefit, Vtail, accounts for over 47% of the total adaptation value, a component overlooked by expected-loss approaches. This paper advances the literature on real options, climate finance, and stochastic optimization by presenting the first rigorous treatment of adaptation timing through a stopping-time approach with an explicit role for regulatory capital.
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