Probabilistic Models of Economic Dynamics with Endogenous Changes of Technology

We study economic dynamics models in which technological changes (the emergence of new technological modes) are related to the expenditures of resources taken from the sphere of material production. The production sphere is described by the dynamic model "input-output," which in turn is defined in terms of technological sets or production functions. New technologies arise from the sphere of "technological progress" (TP), described by a similar model. The instants at which new technologies emerge are taken to be random variables, whose characteristics depend upon the functioning of the TP sphere. So, we have the optimization problem of allocating resources between the production and the TP spheres and choosing the corresponding technological modes in the respective spheres. This approach was proposed in Arkin et al. (1976), in which a general scheme for describing economic dynamics models with endogenous TP was formulated in terms of the controlled random processes theory. Two models are considered in this paper. The first is a generalization of the classical Gale model where the probability of technological change at instant t is determined by "funds" accumulated up to that time in the TP sphere. The second model is the stochastic analog of the multisectoral macroeconomic model that was discussed in Zelikina (1977) for the case of continuous time. As in the first model, the production function change is random and is determined by TP funds. The main results discussed in this paper are a description of dual variables (stimulating prices) and the establishment of the related indicators of economic efficiency. In the system of obtained stimulating prices, the estimates of new technologies related to the stochastic nature of the models should be singled out. They have no deterministic analogs

Extension of the Class of Markov Models

In a recent book, the author proposed a new method of solving stochastic control problems, which, unlike the traditional approach, is not based on dynamic programming techniques. The main features of the new method are the extension of the Markov controls and the use of non-Markov controls which depend on the complete history of the process. In this extended control domain the optimal control problem becomes a mathematical programming problem in the space of functions and can be studied using convex analysis. The author first generalizes the Markov control extension theorem for problems with constraints which depend on future time, and then obtains a method for finding the optimal control in convex problems through the solution of the auxiliary mathematical programming problem

Economic Dynamics Models with Innovations: A Probabilistic Approach

The objective of this paper is twofold. First, to include innovation processes with costly implementation (emergence and propagation of new technologies) into the classical theory of economic dynamics models. Second, to show that the transition to the stochastic setting of the problem allows to partially eliminate difficulties due to the discrete nature of innovations' emergence, leading to, in the deterministic case, nonconvex extremal problems. This presentation is based on the classical Gale model in the simplest situation when the technology is extended only once. In this case, a non-standard, two-stage stochastic programming problem with controlled measure is shown to emerge. The main results consist of a description of the structure of the dual variables (stimulating prices) and some related indicators of economic efficiency taking into account the probabilistic nature of the model. The major role in the system of economic indicators constructed is played by the new technology estimates arising due to the consideration of uncertainty and the lack of deterministic counterparts

Change in Economic Mechanism: Model of Evolutionary Transition from Budgets Regulation to Competitive Market

In the framework of dynamic equilibrium theory we propose a model of evolutionary transition from Economy with centralized budgets regulation to Market Economy (with self-financing). It is assumed that information about possible change of economic mechanism affects essentially on behavior of agents. Duration of transition period is regarded as a random variable. We study conditions when such transition allows firms to adapt their plans to future market and guarantees an existence of equilibrium paths. It is also discussed the case of Shock (instantaneous transition) which may bring to bankruptcy, jump of prices and deficit

Stochastic Optimization; Proceedings of the International Conference, Kiev, USSR, September 1984

The purpose of this conference, which was attended by 240 scientists from 20 countries, was to survey the latest developments in the field of controlled stochastic processes, stochastic programming, control under incomplete information and applications of stochastic optimization techniques to problems in economics, engineering, modeling of energy systems, etc. The conference reflected a number of recent important developments in the field, notably new results in control theory with incomplete information, stochastic maximum principle, new numerical techniques for stochastic programming and related software, application of probabilistic methods to the modeling of the economy. The contributions to this book are divided into three categories: (1) Controlled stochastic processes; (2) Stochastic extremal problems; and (3) Stochastic optimization problems with incomplete information

Stochastic programming approaches to stochastic scheduling

Practical scheduling problems typically require decisions without full information about the outcomes of those decisions. Yields, resource availability, performance, demand, costs, and revenues may all vary. Incorporating these quantities into stochastic scheduling models often produces diffculties in analysis that may be addressed in a variety of ways. In this paper, we present results based on stochastic programming approaches to the hierarchy of decisions in typical stochastic scheduling situations. Our unifying framework allows us to treat all aspects of a decision in a similar framework. We show how views from different levels enable approximations that can overcome nonconvexities and duality gaps that appear in deterministic formulations. In particular, we show that the stochastic program structure leads to a vanishing Lagrangian duality gap in stochastic integer programs as the number of scenarios increases.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44935/1/10898_2004_Article_BF00121682.pd

Stochastic Optimization approach to dynamic problems with jump changing structure

Abstract: Lecture Notes in Economics and Mathematical Systems. V.458. 1998. Springer