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

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 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

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 payoffs are exogenous and depend only on the underlying stochastic process of states of the world. The present work develops a model where the payoffs are endogenous: they depend on the share of total market wealth invested in the asset

Globally evolutionarily stable portfolio rules,

Abstract The paper examines a dynamic model of a financial market with endogenous asset prices determined by short run equilibrium of supply and demand. Assets pay dividends that are partially consumed and partially reinvested. The traders use fixed-mix investment strategies (portfolio rules), distributing their wealth between assets in fixed proportions. Our main goal is to identify globally evolutionarily stable strategies, allowing an investor to "survive," i.e. to accumulate in the long run a positive share of market wealth, regardless of the initial state of the market. It is shown that there is a unique portfolio rule with this property-an analogue of the famous Kelly (1956) rule of "betting one's beliefs." A game theoretic interpretation of this result is given. JEL-Classification: G11, C61, C62