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, rates suffer a series of finite discontinuities located at random Poissonian times. Jump amplitudes are also random and governed by an arbitrary density. Suc...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/14/1589 |
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| author | Jaume Masoliver Miquel Montero Josep Perelló |
| author_facet | Jaume Masoliver Miquel Montero Josep Perelló |
| author_sort | Jaume Masoliver |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T09:33:07Z |
| format | Article |
| id | doaj.art-1aacc097930e4e3b962b73d7c1e689f7 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T09:33:07Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-1aacc097930e4e3b962b73d7c1e689f72023-11-22T04:19:11ZengMDPI AGMathematics2227-73902021-07-01914158910.3390/math9141589Jump-Diffusion Models for Valuing the Future: Discounting under Extreme SituationsJaume Masoliver0Miquel Montero1Josep Perelló2Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028 Barcelona, SpainDepartament de Física de la Matèria Condensada, Universitat de Barcelona, 08028 Barcelona, SpainDepartament de Física de la Matèria Condensada, Universitat de Barcelona, 08028 Barcelona, SpainWe 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.https://www.mdpi.com/2227-7390/9/14/1589stochastic processesfinanceclimatediscount functionenvironmental econonomicsPoissonian jumps |
| spellingShingle | Jaume Masoliver Miquel Montero Josep Perelló Jump-Diffusion Models for Valuing the Future: Discounting under Extreme Situations Mathematics stochastic processes finance climate discount function environmental econonomics Poissonian jumps |
| title | Jump-Diffusion Models for Valuing the Future: Discounting under Extreme Situations |
| title_full | Jump-Diffusion Models for Valuing the Future: Discounting under Extreme Situations |
| title_fullStr | Jump-Diffusion Models for Valuing the Future: Discounting under Extreme Situations |
| title_full_unstemmed | Jump-Diffusion Models for Valuing the Future: Discounting under Extreme Situations |
| title_short | Jump-Diffusion Models for Valuing the Future: Discounting under Extreme Situations |
| title_sort | jump diffusion models for valuing the future discounting under extreme situations |
| topic | stochastic processes finance climate discount function environmental econonomics Poissonian jumps |
| url | https://www.mdpi.com/2227-7390/9/14/1589 |
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