Prices on Information and Stochastic Insurance Models

This paper is closely connected with the studies on decision making under uncertainty, particularly with the stochastic optimization problems that are investigated in the Adaptation and Optimization Project of the System and Decision Sciences Program. The paper deals with some economic models in which it appears possible to formalize the notion of the price on information concerning the problem parameters. Insurance models under uncertainty are studied here with more detail

The Strategic Exploitation of Limited Information and Opportunity in Networked Markets

This paper studies the effect of constraining interactions within a market. A model is analysed in which boundedly rational agents trade with and gather information from their neighbours within a trade network. It is demonstrated that a trader’s ability to profit and to identify the equilibrium price is positively correlated with its degree of connectivity within the market. Where traders differ in their number of potential trading partners, well-connected traders are found to benefit from aggressive trading behaviour.Where information propagation is constrained by the topology of the trade network, connectedness affects the nature of the strategies employed

Arbitrage and deflators in illiquid markets

This paper presents a stochastic model for discrete-time trading in financial markets where trading costs are given by convex cost functions and portfolios are constrained by convex sets. The model does not assume the existence of a cash account/numeraire. In addition to classical frictionless markets and markets with transaction costs or bid-ask spreads, our framework covers markets with nonlinear illiquidity effects for large instantaneous trades. In the presence of nonlinearities, the classical notion of arbitrage turns out to have two equally meaningful generalizations, a marginal and a scalable one. We study their relations to state price deflators by analyzing two auxiliary market models describing the local and global behavior of the cost functions and constraints

Local stability analysis of a stochastic evolutionary financial market model with a risk-free asset

This paper introduces and analyzes an evolutionary model of a financial market with a risk-free asset. Focus is on the study of local stability of the wealth dynamics through the application of recent results on the linearization and stability of random dynamical systems (Evstigneev, Pirogov and Schenk-Hoppé, Proceedings of the American Mathematical Society 139, 1061-1072, 2011). Conditions are derived for the linearization of the model at an equilibrium state which ensure local convergence of sample paths to this equilibrium. The paper also shows that the concept of local stability is closely related to the notion of evolutionary stability. A locally evolutionarily stable investment strategy in the evolutionary model with a risk-free asset is derived, extending previous research. The method illustrated here is applicable for the analysis of manifold economic and financial dynamic models involving randomness

Noncooperative games in networks: Stability and sensitivity of equilibrium

Abstract: Complementarity and variational problems. State of the Art. M.C.Ferris and J.S.Pang, eds. SIAM, Philadelphia, 1997

Rapid growth paths in multivalued dynamical systems generated by homogeneous convex stochastic operators

Abstract: / Setvalued Analysis. 1998. V.6

Multivalued dynamical systems generated by homogeneous convex stochastic operators

Abstract: / Dynamical Systems, University of Bremen, 1997