On Dynkin's model of economic equilibrium under uncertainty.

The article analyzes the Dynkin (1975) stochastic model of economic equilibrium. We solve a question regarding this model that was open for a long time. We provide arguments yielding a complete proof of Dynkin's existence theorem for equilibrium paths.Dynkin stochastic model;

On Dynkin's model of economic equilibrium under uncertainty

The article analyzes the Dynkin (1975) stochastic model of economic equilibrium. We solve a question regarding this model that was open for a long time. We provide arguments yielding a complete proof of Dynkin's existence theorem for equilibrium paths.

On Zermelo's theorem

A famous result in game theory known as Zermelo's theorem says that "in chess either White can force a win, or Black can force a win, or both sides can force at least a draw". The present paper extends this result to the class of all finite-stage two-player games of complete information with alternating moves. It is shown that in any such game either the first player has a winning strategy, or the second player has a winning strategy, or both have unbeatable strategies

Volatility-induced Growth in Financial Markets.

We show that the volatility of prices, which is usually regarded as an impediment for financial growth, may serve as a cause of it.

On the fundamental theorem of asset pricing: random constraints and bang-bang no-arbitrage criteria

The paper generalizes and refines the Fundamental Theorem of Asset Pricing of Dalang, Morton and Willinger in the following two respects: (a) the result is extended to a model with portfolio constraints; (b) versions of the no-arbitrage criterion based on the bang-bang principle in control theory are developed.no arbitrage criteria, portfolio constraints, supermartingale measures, bang-bang control

Evolutionary stable stock markets

Summary.: This paper shows that a stock market is evolutionary stable if and only if stocks are evaluated by expected relative dividends. Any other market can be invaded in the sense that there is a portfolio rule that, when introduced on the market with arbitrarily small initial wealth, increases its market share at the incumbent's expense. This mutant portfolio rule changes the asset valuation in the course of time. The stochastic wealth dynamics in our evolutionary stock market model is formulated as a random dynamical system. Applying this theory, necessary and sufficient conditions are derived for the evolutionary stability of portfolio rules when relative dividend payoffs follow a stationary Markov process. These local stability conditions lead to a unique evolutionary stable portfolio rule according to which assets are evaluated by expected relative dividends (with respect to the objective probabilities

Evolutionary Finance: A model with endogenous asset payoffs

Evolutionary Finance (EF) explores financial markets as evolving biological systems. Investors pursuing diverse investment strategies compete for the market capital. Some "survive" and some "become extinct". A central goal is to identify evolutionary stable (in one sense or another) investment strategies. The problem is analyzed in a framework combining stochastic dynamics and evolutionary game theory. Most of the models currently considered in EF assume that asset payo¤s are exogenous and depend only on the underlying stochastic process of states of the world. The present work develops a model where the payo¤s are endogenous: they depend on the share of total market wealth invested in the asset