Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling

The theory of existence of equilibrium with short-selling is reconsidered under risk and ambiguity modelled by risk averse variational preferences. A sufficient condition for existence of efficient allocations is that the relative interiors of the risk adjusted sets of expectations overlap. This condition is necessary if agents are not risk neutral at extreme levels of wealths either positive or negative. It is equivalent to the condition that there does not exist mutually compatible trades, with non negative expected value with respect to any risk adjusted prior, strictly positive for some agent and some prior. It is shown that the more uncertainty averse and the more risk averse the agents, the more likely are efficient allocations and equilibria to exist.Uncertainty;risk;common prior;equilibria with shortselling;Variational preferences

No-arbitrage, overlapping sets of priors and the existence of efficient allocations and equilibria in the presence of risk and ambiguity

The theory of existence of equilibrium with short-selling is reconsidered under risk and ambiguity modelled by risk averse variational preferences. A sufficient condition for existence of efficient allocations is that the relative interiors of the risk adjusted sets of expectations overlap. This condition is necessary if agents are not risk neutral at extreme levels of wealths either positive or negative. It is equivalent to the condition that there does not exist mutually compatible trades, with non negative expected value with respect to any risk adjusted prior, strictly positive for some agent and some prior. It is shown that the more uncertainty averse and the more risk averse, the more likely are efficient allocations and equilibria to exist.Uncertainty, risk, common prior, equilibria with short-selling, variational preferences.

Evaluation of macroeconomic models for financial stability analysis

As financial stability has gained focus in economic policymaking, the demand for analyses of financial stability and the consequences of economic policy has increased. Alternative macroeconomic models are available for policy analyses, and this paper evaluates the usefulness of some models from the perspective of financial stability. Financial stability analyses are complicated by the lack of a clear and consensus definition of ‘financial stability’, and the paper concludes that operational definitions of this term must be expected to vary across alternative models. Furthermore, since assessment of financial stability in general is based on a wide range of risk factors, one can not expect one single model to satisfactorily capture all the risk factors. Rather, a suite of models is needed. This is in particular true for the evaluation of risk factors originating and developing inside and outside the financial system respectively.Financial stability; Banks; Default; Macroeconomic models; Policy

Radner Equilibria under Ambiguous Volatility

Beißner P. Radner Equilibria under Ambiguous Volatility. Center for Mathematical Economics Working Papers. Vol 493. Bielefeld: Center for Mathematical Economics; 2013.The present paper considers a class of general equilibrium economies when the primitive uncertainty model features uncertainty about continuous-time volatility. This requires a set of mutually singular priors, which do not share the same null sets. For this setting we introduce an appropriate commodity space and the dual of linear and continuous price systems. All agents in the economy are heterogeneous in their preference for uncer- tainty. Each utility functional is of variational type. The existence of equi- librium is approached by a generalized excess utility fixed point argument. Such Arrow-Debreu allocations can be implemented into a Radner economy with continuous-time trading. Effective completeness of the market spaces al- ters to an endogenous property. Only mean unambiguous claims equivalently satisfying the classical martingale representation property build the marketed space

Evaluation of macroeconomic models for financial stability analysis

As financial stability has gained focus in economic policymaking, the demand for analyses of financial stability and the consequences of economic policy has increased. Alternative macroeconomic models are available for policy analyses, and this paper evaluates the usefulness of some models from the perspective of financial stability. Financial stability analyses are complicated by the lack of a clear and consensus definition of ‘financial stability’, and the paper concludes that operational definitions of this term must be expected to vary across alternative models. Furthermore, since assessment of financial stability in general is based on a wide range of risk factors, one can not expect one single model to satisfactorily capture all the risk factors. Rather, a suite of models is needed. This is in particular true for the evaluation of risk factors originating and developing inside and outside the financial system respectively.Financial stability; Banks; Default; Macroeconomic models; Policy

Coherent Price Systems and Uncertainty-Neutral Valuation

We consider fundamental questions of arbitrage pricing arising when the uncertainty model is given by a set of possible mutually singular probability measures. With a single probability model, essential equivalence between the absence of arbitrage and the existence of an equivalent martingale measure is a folk theorem, see Harrison and Kreps (1979). We establish a microeconomic foundation of sublinear price systems and present an extension result. In this context we introduce a prior dependent notion of marketed spaces and viable price systems. We associate this extension with a canonically altered concept of equivalent symmetric martingale measure sets, in a dynamic trading framework under absence of prior depending arbitrage. We prove the existence of such sets when volatility uncertainty is modeled by a stochastic differential equation, driven by Peng's G-Brownian motions

Arbitrage and asset market equilibrium in infinite dimensional economies with risk-averse expected utilities

We consider a model with an infinite numbers of states of nature, von Neumann - Morgenstern utilities and where agents have different prob- ability beliefs. We show that no-arbitrage conditions, defined for finite dimensional asset markets models, are not sufficient to ensure existence of equilibrium in presence of an infinite number of states of nature. How- ever, if the individually rational utility set U is compact, we obtain an equilibrium. We give conditions which imply the compactness of U. We give examples of non-existence of equilibrium when these conditions do not hold

Microeconomic theory of financial markets under volatility uncertainty

Beißner P. Microeconomic theory of financial markets under volatility uncertainty. Bielefeld: Bielefeld University; 2013

Macroeconomics and Finance: The Role of the Stock Market

The treatment of the stock market in finance and macroeconomics exemplifies many of the important differences in perspective between the two fields. In finance, the stock market is the single most important market with respect to corporate investment decisions. In contrast, macroeconomic modelling and policy discussion assign a relatively minor role to the stockmarket in investment decisions. This paper explores four possible explanations for this neglect and concludes that macro analysis should give more attention to the stock market. Despite the frequent jibe that "the stockmarket has forecast ten of the last six recessions," the stock market is in fact a good predictor of the business cycle and the components of GNP. We examine the relative importance of the required return on equity compared with the interest rate in the determination of the cost of capital, and hence,investment. In this connection, we review the empirical success of the Q theory of investment which relates investment to stock market evaluations of firms. One of the explanations for the neglect of the stock market in macroeconomics may be the view that because the stock market fluctuates excessively, rational managers will pay little attention to the market informulating investment plans. This view is shown to be unfounded by demonstrating that rational managers will react to stock price changes even if the stock market fluctuates excessively. Finally, we review the extremely important issue of whether the market does fluctuate excessively, and conclude that while not ruled out on a priori theoretical grounds, the empirical evidence for such excess fluctuations has not been decisive.