Viability and Equilibrium in Securities Markets with Frictions

In this paper we study some foundational issues in the theory of asset pricing with market frictions. We model market frictions by letting the set of marketed contingent claims (the opportunity set) be a convex set, and the pricing rule at which these claims are available be convex. This is the reduced form of multiperiod securities price models incorporating a large class of market frictions. It is said to be viable as a model of economic equilibrium if there exist price-taking maximizing agents who are happy with their initial endowment, given the opportunity set, and hence for whom supply equals demand. This is equivalent to the existence of a positive linear pricing rule on the entire space of contingent claims - an underlying frictionless linear pricing rule - that lies below the convex pricing rule on the set of marketed claims. This is also equivalent to the absence of asymptotic free lunches - a generalization of opportunities of arbitrage. When a market for a non marketed contingent claim opens, a bid-ask price pair for this claim is said to be consistent if it is a bid-ask price pair in at least a viable economy with this extended opportunity set. If the set of marketed contingent claims is a convex cone and the pricing rule is convex and sublinear, we show that the set of consistent prices of a claim is a closed interval and is equal (up to its boundary) to the set of its prices for all the underlying frictionless pricing rules. We also show that there exists a unique extended consistent sublinear pricing rule - the supremum of the underlying frictionless linear pricing rules - for which the original equilibrium does not collapse, when a new market opens, regardless of preferences and endowments. If the opportunity set is the reduced form of a multiperiod securities market model, we study the closedness of the interval of prices of a contingent claim for the underlying frictionless pricing rules

Some economic remarks on arbitrage theory

Today's primarily mathematically oriented arbitrage theory does not address some economically important aspects of pricing. These are, first, the implicit conjecture that there is 'the' price of a portfolio, second, the exact formulation of no-arbitrage, price reproduction, and positivity of the pricing rule under short selling constraints, third, the explicit assumption of a nonnegative riskless interest rate, and fourth, the connection between arbitrage theory (that is almost universal pricing theory) and special pricing theories. Our article proposes the following answers to the above issues: The first problem can be solved by introducing the notion of 'physical' no-arbitrage, the second one by formulating the concept of 'actively' traded portfolios (that is non-dominated portfolios) and by requiring that there is a minimum price for actively traded portfolios and therefore for every admissible portfolio, and the third one by combining the 'invisible' asset 'cash' with the idea of actively traded portfolios - a riskless asset with a rate of return less than zero can never be actively traded in the presence of cash. Finally, the connection between arbitrage theory and special pricing theories ('law-of-one-price-oriented' and 'utility-oriented' pricing) consists in the fact that special pricing theories merely concretize arbitrage theory using different assumptions. --

Exploiting arbitrage requires short selling

We show that in a financial market given by semimartingales an arbitrage opportunity, provided it exists, can only be exploited through short selling. This finding provides a theoretical basis for differences in regulation for financial services providers that are allowed to go short and those without short sales. The privilege to be allowed to short sell gives access to potential arbitrage opportunities, which creates by design a bankruptcy risk.Comment: 13 page

Sharpe Ratio Maximization and Expected Utility when Asset Prices have Jumps

We analyze portfolio strategies which are locally optimal, meaning that they maximize the Sharpe ratio in a general continuous time jump-diffusion framework. These portfolios are characterized explicitly and compared to utility based strategies. In the presence of jumps, maximizing the Sharpe ratio is shown to be generally inconsistent with maximizing expected utility, but this is shown to depend strongly on market completeness and whether event risk is priced.

General equilibrium and fixed point theory : a partial survey

Focusing mainly on equilibrium existence results, this paper emphasizes the role of fixed point theorems in the development of general equilibrium theory, as well for its standard definition as for some of its extensions.Fixed point, equilibrium, quasiequilibrium, abstract economy, Clarke's normal cone, financial equilibrium, Grassmanian manifold, degree theory.

General equilibrium in asset markets with or without short-selling

Equilibrium Theory;Assets

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

Liquidity and the threat of fraudulent assets

We study an over-the-counter (OTC) market with bilateral meetings and bargaining where the usefulness of assets, as means of payment or collateral, is limited by the threat of fraudulent practices. We assume that agents can produce fraudulent assets at a positive cost, which generates endogenous upper bounds on the quantity of each asset that can be sold, or posted as collateral in the OTC market. Each endogenous, asset-specific, resalability constraint depends on the vulnerability of the asset to fraud, on the frequency of trade, and on the current and future prices of the asset. In equilibrium, the set of assets can be partitioned into three liquidity tiers, which differ in their resalability, their prices, their sensitivity to shocks, and their responses to policy interventions. The dependence of an asset’s resalability on its price creates a pecuniary externality, which leads to the result that some policies commonly thought to improve liquidity can be welfare reducing.Liquidity (Economics) ; Fraud ; Asset pricing