Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 10 June 2021 / Approved: 14 June 2021 / Online: 14 June 2021 (07:47:51 CEST)

A peer-reviewed article of this Preprint also exists.

Masoliver, J.; Montero, M.; Perelló, J. Jump-Diffusion Models for Valuing the Future: Discounting under Extreme Situations. Mathematics 2021, 9, 1589. Masoliver, J.; Montero, M.; Perelló, J. Jump-Diffusion Models for Valuing the Future: Discounting under Extreme Situations. Mathematics 2021, 9, 1589.

Journal reference: Mathematics 2021, 9, 1589
DOI: 10.3390/math9141589

Abstract

We develop the process of discounting when underlying rates follow a jump-diffusion process, that is, when, in addition of 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 continous time random walk.

Subject Areas

stochastic processes; finance; climate; discount function; environmental econonomics; Poissonian jumps; Ornstein-Uhlenbeck process; interest rates; asymptotics

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