Abstract. We consider the problem of stopping a diffusion process with a payoff functional involving probability distortion. The problem is inherently time-inconsistent as the level of distortion of a same event changes over time. We study stopping decisions of naïve agents who reoptimize continuously in time, as well as equilibrium strategies of sophisticated agents who anticipate but lack control over their future selves’ behaviors. When the state process is one dimensional and the payoff functional satisfies some regularity conditions, we prove that any equilibrium can be obtained as a fixed point of an operator. This operator represents strategic reasoning that takes the future selves’ behaviors into account. In particular, we show how such strategic reasoning may turn a naïve agent into a sophisticated one. Finally, when the diffusion process is a geometric Brownian motion we derive stopping strategies of these two types of agent for various parameter specifications of the problem, illustrating rich behaviors beyond the extreme ones such as “never-stopping” or “never-starting”.
In this paper, we examine how central banks and financial supervisors are approaching the topic of BRFR in relation to climate-related financial risk. We argue that policymakers should focus upon the broader concept of systemic environmental-financial risks to account for the interactions and trade-offs between both domains of biodiversity and climate change.
This article studies the exploitation of recyclable exhaustible resources such as metals that are crucial for the energy transition or phosphorus that is crucial for agricultural production. We use a standard Hotelling model of resource exploitation that includes a primary sector and a recycling sector.