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2021-07-06

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cc-by (c) Masoliver, Jaume, 1951- et al., 2021
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/178953

Jump-diffusion models for valuing the future: Discounting under extreme situations

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https://doi.org/10.3390/math9141589

Abstract

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.

Subject

Processos estocàstics, Finances, Tarifes, Clima

Subject (English)

Stochastic processes, Finance, Rates, Climate

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Articles publicats en revistes (Física de la Matèria Condensada)
Articles publicats en revistes (Institut de Recerca en Sistemes Complexos (UBICS))

Citation

MASOLIVER, Jaume, MONTERO TORRALBO, Miquel and PERELLÓ, Josep. Jump-diffusion models for valuing the future: Discounting under extreme situations. Mathematics. 2021. Vol. 2021, num. 9, pags. 1589-1-1589-26. ISSN 2227-7390. [consulted: 11 of June of 2026]. Available at: https://hdl.handle.net/2445/178953

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