Risk trading and endogenous probabilities in investment equilibria

A risky design equilibrium problem is an equilibrium system that involves N designers who invest in risky assets, such as production plants, evaluate these using convex or coherent risk measures, and also trade financial securities in order to manage their risk. Our main finding is that in a complete risk market - when all uncertainties can be replicated by financial products - a risky design equilibrium problem collapses to what we call a risky design game, i.e., a stochastic Nash game in which the original design agents act as risk neutral and there emerges an additional system risk agent. The system risk agent simultaneously prices risk and determines the probability density used by the other agents for their risk neutral evaluations. This situation is stochastic-endogenous: the probability density used by agents to value uncertain investments is endogenous to the risky design equilibrium problem. This result is most striking when design agents use coherent risk measures in which case the intersection of their risk sets turns out to be a risk set for the system risk agent, thereby extending existing results for risk markets. We also investigate existence of equilibria in both the complete and incomplete cases

Risk trading and endogenous probabilities in investment equilibria

A risky design equilibrium problem is an equilibrium system that involves N designers who invest in risky assets, such as production plants, evaluate these using convex or coherent risk measures, and also trade financial securities in order to manage their risk. Our main finding is that in a complete risk market - when all uncertainties can be replicated by financial products - a risky design equilibrium problem collapses to what we call a risky design game, i.e., a stochastic Nash game in which the original design agents act as risk neutral and there emerges an additional system risk agent. The system risk agent simultaneously prices risk and determines the probability density used by the other agents for their risk neutral evaluations. This situation is stochastic-endogenous: the probability density used by agents to value uncertain investments is endogenous to the risky design equilibrium problem. This result is most striking when design agents use coherent risk measures in which case the intersection of their risk sets turns out to be a risk set for the system risk agent, thereby extending existing results for risk markets. We also investigate existence of equilibria in both the complete and incomplete cases

Selection in asset markets: the good, the bad, and the unknown

In this paper, we use a series of simple examples to illustrate how wealth-driven selection works in a market for Arrow securities. Our analysis delivers both a good and a bad message. The good message is that, when traders invest constant fractions of their wealth in each asset and have equal consumption rates, markets are informationally effcient: the best informed agent is rewarded and asset prices eventually reflect this information. However, and this is the bad message, when asset demands are not constant fractions of wealth but dependent upon prices, markets might behave suboptimally. In this case, asymptotic prices depend on preferences and beliefs of the whole ecology of traders and do not, in general, reflect the best available information. We show that the key difference between the two cases lies in the local, i.e. price dependent, versus global nature of wealth-driven selection.Market Selection; Evolutionary Finance;Informational Efficiency; Asset Pricing; CRRA Preferences

Complementarities in information acquisition with short-term trades

In a financial market where agents trade for short-term profit and where news can increase the uncertainty of the public belief, there are strategic complementarities in the acquisition of private information and, if the cost of information is sufficiently small, a continuum of equilibrium strategies. Imperfect observation of past prices reduces the continuum of Nash equilibria to a Strongly Rational-Expectations Equilibrium. In that equilibrium, there are two sharply different regimes for the evolution of the price, the volume of trade, and information acquisition.Endogenous information, short-term gain, microstructure, strategic complementarity, multiple equilibria, Strongly Rational-Expectations Equilibrium, trading frenzies

The economics of global environmental risk

This chapter focusses on global environmental risks such as climate change, an issue that must be confronted as we move into the future. It proposes sound principles of risk management that make sense in today's society generally, going beyond their role of averting and hedging climate risks. This chapter is about these and related questions. In attempting to answer them, it deals with different aspects of the theory of risk-bearing. I explain current responses to global change, focusing on the new challenges: human-induced or endogenous risks, including potentially catastrophic risks, which are not adequately treated by traditional economic analysis. In summary, we are dealing with risks that have two major new characteristics: they are endogenous and potentially catastrophic. In addition, climate risks have three more conventional features: they are poorly understood, correlated and irreversible. In all cases, this chapter proposes ways to advance our understanding of the problems. This chapter proposes ways to evaluate decisions under endogenous and potentially catastrophic risks, and incorporates often neglected features of correlated, poorly understood and irreversible risks. The analysis proposed here opens new ways of thinking and at the same time poses new challenges. At the end I indicate new areas of research.risk; global environment; climate change; endogenous risk; catastrophic risk; risk management; mathematical modeling; endogenous uncertainty; policy

Heterogeneous Agent Models in Economics and Finance, In: Handbook of Computational Economics II: Agent-Based Computational Economics, edited by Leigh Tesfatsion and Ken Judd , Elsevier, Amsterdam 2006, pp.1109-1186.

This chapter surveys work on dynamic heterogeneous agent models (HAMs) in economics and finance. Emphasis is given to simple models that, at least to some extent, are tractable by analytic methods in combination with computational tools. Most of these models are behavioral models with boundedly rational agents using different heuristics or rule of thumb strategies that may not be perfect, but perform reasonably well. Typically these models are highly nonlinear, e.g. due to evolutionary switching between strategies, and exhibit a wide range of dynamical behavior ranging from a unique stable steady state to complex, chaotic dynamics. Aggregation of simple interactions at the micro level may generate sophisticated structure at the macro level. Simple HAMs can explain important observed stylized facts in financial time series, such as excess volatility, high trading volume, temporary bubbles and trend following, sudden crashes and mean reversion, clustered volatility and fat tails in the returns distribution.

Asset price volatilities and trading volumes in heterogeneous agent economies

Apart from the risk premium of equity over bonds, volatility of asset prices and trading volumes are two aspects of the already developed general equilibrium asset pricing theory that fail to show any resemblance with real data. The assumption of agent homogeneity has been relaxed in a number of studies where agents face uninsurable income shocks but fail to provide a consistent explanation that addresses all issues. This study assumes a dynamically complete asset market with two states and two assets, where the agents are allowed to be heterogeneous either in terms of their risk preferences, or in terms of their beliefs for the probabilities of the exogenous shock. The assumption that the (logarithm of the) aggregate dividend follows an autoregressive process with an iid state dependent shock, helps us construct a non-trivial equilibrium in which the endogenously determined wealth distribution across agents is part of the economy's state vector. Qualitative results show that this kind of setup works in the right direction in all issues addressed, while quantitative results are produced using a projection method as well as a variant of the Krusell and Smith method

Do Miracles Lead to Crises?: An Informational Frictions Explanation to Emerging Market Financial Crises

financial crises, emerging markets, informational frictions, signal extraction

Instabilities and Robust Control in Fisheries

Demand and supply analysis in fisheries often indicates the presence of instabilities and multiple equilibria, both in open access conditions and in the socially optimal solution. The associated management problems are further intensified by uncertainty on the evolution of the resource stock or on demand conditions. In this paper the fishery management problem is handled using robust optimal control, where the objective is to choose a harvesting rule that will work, in the sense of preventing instabilities and overfishing, under a range of admissible specifications for the stock recruitment equation. The paper derives robust harvesting rules, leading to a unique equilibrium, which could be used to design policy instruments such as robust quota systems.Fishery Management, Multiple Equilibria, Instabilities, Robust Control, Robust Harvesting Rules