Jump-Diffusion Models for Valuing the Future: Discounting under Extreme Situations

We develop the process of discounting when underlying rates follow a jump-diffusion process, that is, when, in addition to diffusive behavior, suffer series finite discontinuities located at random Poissonian times. Jump amplitudes are also and governed by an arbitrary density. Such model may describe economic evolution, specially extreme situations occur (pandemics, global wars, etc.). When, between jumps, dynamical evolution is Ornstein–Uhlenbeck diffusion we obtain exact explicit expressions for discount function long-run rate show presence drastically reduce rate, fact has significant consequences environmental planning. discuss as specific example case described continuous time walk.