A CONTINUOUS TIME APPROXIMATION OF AN EVOLUTIONARY STOCK MARKET MODEL

2007 ◽  
Vol 10 (07) ◽  
pp. 1229-1253 ◽  
Author(s):  
BORIS BUCHMANN ◽  
STEFAN WEBER
Keyword(s):  
Integral Equation ◽  
Continuous Time ◽  
Lyapunov Functions ◽  
Asset Returns ◽  
Market Model ◽  
Market Selection ◽  
Time Approximation ◽  
Long Run ◽  
Payoff Structure ◽  
Autonomous Ordinary Differential Equation

We derive a continuous time approximation of the evolutionary market selection model of Blume and Easley (1992). Conditions on the payoff structure of the assets are identified that guarantee convergence. We show that the continuous time approximation equals the solution of an integral equation in a random environment. For constant asset returns, the integral equation reduces to an autonomous ordinary differential equation. We analyze its long-run asymptotic behavior using techniques related to Lyapunov functions, and compare our results to the benchmark of profit-maximizing investors.

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 The economic market outcomes and income distribution when capital is not homogeneous

2019 ◽  
Vol 1 (1) ◽  
pp. 38-56
Author(s):  
Ahmet Özçam
Keyword(s):  
Measurement Problem ◽  
Physical Capital ◽  
Threshold Level ◽  
Market Model ◽  
Economic Market ◽  
Constant Elasticity ◽  
Content Type ◽  
Macroeconomic Analysis ◽  
Long Run ◽  
Short Run

Purpose An aggregate production function has been used in macroeconomic analysis for a long time, even though it seems that it is conceptually confusing and problematic. The purpose of this paper is to argue that the measurement problem related to the heterogenous capital input that exists in macroeconomics is also relevant to microeconomic market situations. Design/methodology/approach The author constructed a microeconomic market model to address both the problems of the measurement of the physical capital and of substitutability between labor and capital in the short run using two types of technologies: labor neutral and labor reducing. The author proposed that labor and physical capital inputs are complementary in the short run and can become substitutes only in the long run when the technology advances. Findings The author found that even if the technology improves at a fast rate over time, there are then diminishing returns of profits to technology and an upper limit to profits. Moreover, the author showed that under the labor-reducing technology, labor class earns more initially as technology improves, but their incomes start declining after some threshold level of passage of time. Originality/value The author cautioned the applied researcher that the estimated labor and capital coefficients of generalized Cobb–Douglas and constant elasticity of substitution of types of production functions could not be interpreted as partial elasticities of labor and capital if in reality the data come from fixed-proportions types of processes.

Long-Run Stockholder Consumption Risk and Asset Returns

2008 ◽  
Author(s):  
Annette Vissing-Jorgensen ◽  
Christopher J. Malloy ◽  
Tobias J. Moskowitz
Keyword(s):  
Asset Returns ◽  
Long Run ◽  
Consumption Risk

A Fluid EOQ Model with Markovian Environment

2015 ◽  
Vol 52 (02) ◽  
pp. 473-489
Author(s):  
Yonit Barron
Keyword(s):  
Continuous Time ◽  
Inventory Level ◽  
Continuous Time Markov Chain ◽  
Holding Costs ◽  
Eoq Model ◽  
Long Run ◽  
Average Criterion ◽  
Production Inventory ◽  
Finite State ◽  
Cost Functionals

We consider a production-inventory model operating in a stochastic environment that is modulated by a finite state continuous-time Markov chain. When the inventory level reaches zero, an order is placed from an external supplier. The costs (purchasing and holding costs) are modulated by the state at the order epoch time. Applying a matrix analytic approach, fluid flow techniques, and martingales, we develop methods to obtain explicit equations for these cost functionals in the discounted case and under the long-run average criterion. Finally, we extend the model to allow backlogging.

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