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

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1589
Author(s):  
Jaume Masoliver ◽  
Miquel Montero ◽  
Josep Perelló
Keyword(s):  
Diffusion Process ◽  
Discount Rate ◽  
Continuous Time ◽  
Environmental Planning ◽  
Dynamical Evolution ◽  
Jump Diffusion ◽  
Economic Evolution ◽  
Discount Function ◽  
Long Run ◽  
Future Discounting

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.

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

2021 ◽  
Author(s):  
Jaume Masoliver ◽  
Miquel Montero ◽  
Josep Perelló
Keyword(s):  
Random Walk ◽  
Diffusion Process ◽  
Discount Rate ◽  
Environmental Planning ◽  
Dynamical Evolution ◽  
Jump Diffusion ◽  
Economic Evolution ◽  
Discount Function ◽  
Long Run ◽  
Future Discounting

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.

Effect of the Return Policy in a Continuous-Time Newsvendor Problem

2017 ◽  
Vol 34 (06) ◽  
pp. 1750031
Author(s):  
Weiwei Zhang ◽  
Zhongfei Li ◽  
Ke Fu ◽  
Fan Wang
Keyword(s):  
Diffusion Process ◽  
Continuous Time ◽  
Existence And Uniqueness ◽  
Stackelberg Game ◽  
Jump Diffusion ◽  
Newsvendor Problem ◽  
Stackelberg Equilibrium ◽  
Computational Results ◽  
Return Policy ◽  
Demand Rate

This paper studies the stochastic differential Stackelberg game in a continuous-time newsvendor problem with a return policy, in which one supplier sells products to one retailer and the two parties make the decisions sequentially to maximize their own expected profits. When the demand process is a general jump-diffusion process, we provide a general formula for the equilibrium if it exists. When the demand rate is an Ornstein–Uhlenbeck (O–U) process, we prove the existence and uniqueness of the equilibrium and find an explicit expression for the equilibrium. Computational results show that the return policy has significant impact on the Stackelberg equilibrium.

Portfolio Selection with Transaction Costs and Jump-Diffusion Asset Dynamics I: A Numerical Solution

2016 ◽  
Vol 06 (04) ◽  
pp. 1650018 ◽  
Author(s):  
Michal Czerwonko ◽  
Stylianos Perrakis
Keyword(s):  
Diffusion Process ◽  
Transaction Costs ◽  
Portfolio Selection ◽  
Discrete Time ◽  
Continuous Time ◽  
Jump Diffusion ◽  
Numerical Approach ◽  
Proportional Transaction Costs ◽  
Asset Portfolio ◽  
Time Formulation

We derive allocation rules under isoelastic utility for a mixed jump-diffusion process in a two-asset portfolio selection problem with finite horizon in the presence of proportional transaction costs. We adopt a discrete-time formulation, let the number of periods go to infinity, and show that it converges efficiently to the continuous-time solution for the cases where this solution is known. We then apply this discretization to derive numerically the boundaries of the region of no transactions. Our discrete-time numerical approach outperforms alternative continuous-time approximations of the problem.

A Dynamic Analysis of Child Labor with a Variable Rate of Discount: Some Policy Implications

2006 ◽  
Vol 5 (1) ◽  
Author(s):  
Satya P Das ◽  
Rajat Deb
Keyword(s):  
Discount Rate ◽  
Child Labor ◽  
Time Preference ◽  
Infinite Horizon ◽  
Policy Implications ◽  
Poverty Trap ◽  
Variable Rate ◽  
Lump Sum ◽  
Long Run ◽  
Short Run

AbstractThis paper analyzes the problem of child labor in an infinite-horizon dynamic model with a variable rate of time preference and credit constraints. The variability in the rate of time preference leads to the possibility of multiple steady states and a poverty trap. The paper considers the long-run and short-run effects of an array of policies like enrollment subsidy, improvement in primary education infrastructure, lump-sum subsidy, and variations in loan market parameters. We distinguish between policies that reduce child labor in the long run only in the presence of a variable discount rate and other policies which work whether or not the discount rate is variable. Credit-related policies belong to the former group. Policies that reduce child labor and increase family consumption in the long run may have an adverse effect of lowering consumption in the short run.

Sign in / Sign up

Export Citation Format

Share Document