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Jump-diffusion models for valuing the future: Discounting under extreme situations Masoliver, Jaume, 1951- Montero Torralbo, Miquel Perelló, Josep, 1974- Processos estocàstics Finances Tarifes Clima Stochastic processes Finance Rates Climate We develop the process of discounting when underlying rates follow a jump-diffusion process, that is, when, in addition to diffusive behavior, rates suffer a series of finite discontinuities located at random Poissonian times. Jump amplitudes are also random and governed by an arbitrary density. Such a model may describe the economic evolution, specially when extreme situations occur (pandemics, global wars, etc.). When, between jumps, the dynamical evolution is governed by an Ornstein-Uhlenbeck diffusion process, we obtain exact and explicit expressions for the discount function and the long-run discount rate and show that the presence of discontinuities may drastically reduce the discount rate, a fact that has significant consequences for environmental planning. We also discuss as a specific example the case when rates are described by the continuous time random walk. 2021-07-09T08:49:07Z 2021-07-09T08:49:07Z 2021-07-06 2021-07-09T08:49:07Z info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion 2227-7390 https://hdl.handle.net/2445/178953 713111 eng Reproducció del document publicat a: https://doi.org/10.3390/math9141589 Mathematics, 2021, vol. 2021, num. 9, p. 1589-1-1589-26 https://doi.org/10.3390/math9141589 cc-by (c) Masoliver, Jaume, 1951- et al., 2021 https://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess 1 p. application/pdf MDPI Articles publicats en revistes (Física de la Matèria Condensada)