Igor V. Evstigneev

Noncooperative versus cooperative R&D with endogenous spillover rates

This paper deals with a general version of a two-stage model of R&D and product market competition. We provide a thorough generalization of previous results on the comparative performance of noncooperative and cooperative R&D, dispensing in particular with ex-post firm symmetry and linear demand assumptions. We also characterize the structure of profit-maximizing R&D cartels where firms competing in a product market jointly decide R&D expenditure, as well as internal spillover, levels. We establish the firms would essentially always prefer extremal spillovers, and within the context of a standard specification, derive conditions for the optimality of minimal spillover.

Exponential Growth of Fixed-Mix Strategies in Stationary Asset Markets

Abstract. The paper analyzes the long-run performance of dynamic investment strategies based on fixed-mix portfolio rules. Such rules prescribe rebalancing the portfolio by transferring funds between its positions according to fixed (time-independent) proportions. The focus is on asset markets where prices fluctuate as stationary stochastic processes. Under very general assumptions, it is shown that any fixed-mix strategy in a stationary market yields exponential growth of the portfolio with probability one.

Volatility-induced financial growth

We show that the volatility of a price process, which is usually regarded as an impediment to financial growth, can serve as an endogenous factor in its acceleration.

Financial markets. The joy of volatility

Financial markets. The joy of volatility M. A. H. Dempster a; Igor V. Evstigneev b; Klaus Reiner Schenk-Hoppe c a Centre for Financial Research, Statistical Laboratory, University of Cambridge, Cambridge CB5 8AF, UK b Economic Studies, School of Social Sciences, University of Manchester, Manchester, M13 9PL, UK c School of Mathematics and Leeds University Business School, University of Leeds, Leeds, LS2 9JT, UK

The von Neumann-Gale growth model and its stochastic generalization

This paper deals with the deterministic and stochastic versions of the von Neumann-Gale model. Von Neumanns (1937) original concern was to determine a balanced path growing at a maximal rate for a linear and stationary technology and a price system supporting that path. Such a pair (a path and a price system) was called a von Neumann equilibrium. Gale (1956) proposed a version of the model assuming a general, not necessarily linear technology. This generalization led to a rich and interesting theory aimed at the analysis of efficient growth paths and based on the concepts introduced by von Neumann. The theory was developed in the 1950s and 1960s by Rockafellar, Radner, McKenzie, Nikaido, Morishima, and others. Its extension to the stochastic case was an open problem for about three decades, and a substantial progress in this direction was made only in the 1990s. The main results obtained are concerned with stochastic generalizations of a von Neumann equilibrium and efficient paths. Fundamental questions about their existence, uniqueness and stability (turnpike properties) are answered. The chapter gives an account of the achievements in the field and outlines new applications of the von Neumann-Gale model in finance related to asset pricing and hedging in securities markets.

Rapid growth paths in convex-valued random dynamical systems

This paper examines set-valued random dynamical systems defined by convex homogeneous stochastic operators. The operators under consideration transform elements of a cone contained in a space of random vectors into subsets of the cone. We study rapid paths of such dynamical systems, i.e. those paths which maximize (appropriately defined) growth rates at every time period. Questions of existence, uniqueness and asymptotic behavior of infinite rapid trajectories are considered. The study is motivated by problems related to stochastic models of economic growth.

Growing Wealth with Fixed-Mix Strategies

This chapter surveys theoretical research on the long-term performance of fixed-mix investment strategies. These self-financing strategies rebalance the portfolio over time so as to keep constant the proportions of wealth invested in various assets. The main result is that wealth can be grown from volatility. Our findings demonstrate the benefits of active portfolio management and the potential of financial engineering.

CHAPTER 9 – Evolutionary Finance

Publisher Summary This chapter surveys current research and applications of evolutionary finance inspired by Darwinian ideas and random dynamical systems theory. This approach studies the market interaction of investment strategies, and the wealth dynamics it entails in financial markets. The emphasis in this survey was on the motivation and the heuristic justification of the results; technical details were avoided as much as possible. In contrast to the current standard paradigm in economic modeling, this approach is based on random dynamical systems. An equilibrium holds only in the short term, which reflects the model of investment behavior explored in an evolutionary finance approach. Continuous-time evolutionary finance models are the latest development in this field. This approach can be seen as a generalization of the workhorse model of continuous-time financial mathematics. One advantage of this model is the flexibility to have different trade frequencies and changes in dividend payments.

Stochastic Equilibria in von Neumann-Gale Dynamical Systems

The paper examines a class of random dynamical systems related to the classical von Neumann and Gale models of economic dynamics. Such systems are defined in terms of multivalued operators in spaces of random vectors, possessing certain properties of convexity and homogeneity. We establish a general existence theorem for equilibrium, which holds under conditions analogous to the standard deterministic ones. Our results answer questions that remained open for more than three decades.

Equilibrium States of Random Economies with Locally Interacting Agents and Solutions to Stochastic Variational Inequalities in 〈L 1,L ∞ 〉

We study a stochastic model of an economy with locally interacting agents. The basis of the study is a deterministic model of dynamic economic equilibrium proposed by Polterovich. We generalize Polterovichs theory, in particular, in two respects. We introduce stochastics and consider a version of the model with local interactions between the agents. The structure of the interactions is described in terms of random fields on a directed graph. Equilibrium states of the system are solutions to certain variational inequalities in spaces of random vectors. By analyzing these inequalities, we establish an existence theorem for equilibrium, which generalizes and refines a number of previous results.