Risk Sharing in a Network of Transactions: A Public Information Case

In this paper we present a model of a network or an arrangement of transactions that involve a risky transfer of assets. Transactions are generated endogenously. There is a risk in asset transfers and we are concerned with the question of optimal risk management in such a network. Assets in this paper may well be usual commodities and not limited to financial assets. If there is some risk of failure in a transfer from one party to another, should the transfer be done through that arrangement? If so, then what considerations are relevant to determining whether third parties ought to share that risk? Are there conditions under which the general public or the government (in the case of a private arrangement) ought to bear some risk and, if so, what level of compensation would it be appropriate for them to receive? In the present paper, we address these questions by analyzing a schematic, formal, model of a network of transactions.

Efficiency of Stochastic Transfers in a Directed Graph

A mathematical model of a directed graph with stochastic transfers is presented. It will be used to analyze the optimality (or "competitiveness") properties of a network of transactions involving risky transfers of assets in an economic system. These properties are discussed in a model with some specific directed graph structures which result in a decomposition of the graph into parts with "narrow" linkage.

On a Problem of Proving the Existence of an Equilibrium in a Large Economy without Free Disposal: A problem of a purely finitely additive measure arising from the Fatou's lemma in several dimensions

It is well-known in the literature that the free disposability or the desirability of all the commodities is needed to ensure the existence of an equilibrium in a large economy with a continuum of economic agents. This is a stark contrast to the case of economies with a finite number of agents, where an equilibrium can be shown to exist without assuming the free disposability nor the desirability of the commodities in case that negative prices are allowed to coordinate demands and supplies. This difference originates in the fact that feasible allocations to individuals are bounded by the totally available resources in finite economies whereas in economies with an infinite number of agents what each individual can feasibly consume need not be bounded by the average of totally available resources. The purpose of our paper, however, is to show that the assumption of the free disposability nor the desirability of all the commodities is not needed for the existence of an equilibrium even in a large economy with a continuum of economic agents provided that negative prices are allowed and that the preference distribution among the agents satisfy a mild requirement that "if there are unboundedly desirable commodities, they must be unanimously regarded as such by almost all members of the economy.

Monetary Equilibrium with Buying and Selling Price Spread without Transactions Costs

This paper is concerned with the Hahn problem in a general monetary equilibrium model at the terminal period. Under the assumption that an initial endowment allocation is not Pareto optimal it is proved that an equilibrium with a positive value of money exists if traders take buying and selling prices of commodities as given even if transactions costs are not explicitly required in the buying and selling activities of traders in commodity markets. This result seems to suggest two interpretations. One is that a standard monetary equilibrium concept must be strengthened so as to explicitly require an arbitrage-free property of bid-ask spreads of commodity prices vis-a-vis transactions costs. The second interpretation is that a model in which traders take distinct buying and selling prices as given although no transactions costs are required can be thought of as a way to make tax payments required by an external authority in classical papers endogenous in the form of an indirect taxation.

Indeterminacy of Buying and Selling Price Spread in Monetary Equilibrium without Transactions Costs

In this paper we report an existence result in a general monetary equilibrium model with buying and selling price spread but without transactions costs. Under the assumption that an initial endowment allocation is not Pareto optimal it is proved that an equilibrium with a positive value of money exists if traders take buying and selling prices of commodities as given even if transactions costs are not explicitly required in the buying and selling activities of traders in commodity markets. This result points to an indeterminacy problem arising from existing general equilibrium models with transaction technologies.

Interim Core Concepts for a Bayesian Pure Exchange Economy

The private information case of a Bayesian pure exchange economy is studied. The Bayesian incentive-compatible coarse core is proved to be nonempty. On the other hand, the Bayesian incentivecompatible interim core may be empty, even for Bayesian pure exchange economies satisfying the traditional (neoclassical) assumptions. A sufficient condition for the latter's nonemptiness is established; the condition specifies relationships among effects of different type pro-files.

"Efficient Static Replication of European Options under Exponential Levy Models"

This paper proposes a new scheme for the static replication of European options and their portfolios. First, we derive a general approximation formula for efficient static replication as an extension of Carr and Chou [1997, 2002] and Carr and Wu [2002]. Second, we present a concrete procedure for implementing our scheme by applying it to plain vanilla options under exponential LLevy models. Finally, numerical examples in a model developed by Carr, Geman, Madan and Yor [2002] are used to demonstrate that our replication scheme is more efficient and more effective in practice than a standard static replication method.

A New Scheme for Static Hedging of European Derivatives under Stochastic Volatility Models ( Revised in June 2008, Published in "Journal of Futures Markets", Vol.29-5, 397-413, 2009. )

This paper proposes a new scheme for static hedging of European path-independent derivatives under stochastic volatility models. First, we show that pricing European path-independent derivatives under stochastic volatility models is transformed to pricing those under one-factor local volatility models. Next, applying an efficient static replication method for one-dimensional price processes developed by Takahashi and Yamazaki[2007], we present a static hedging scheme for European path-independent derivatives. Finally, a numerical example comparing our method with a dynamic hedging method under the Heston[1993]?s stochastic volatility model is used to demonstrate that our hedging scheme is effective in practice.

Efficient Static Replication of European Options for Exponential Levy Models (Revised in January 2008, Published in "Journal of Futures Markets", Vol.29-1, 1-15, 2009. )

This paper proposes a new scheme for the static replication of European options and their portfolios. First, we derive a general approximation formula for efficient static replication as an extension of Carr and Chou [1997, 2002] and Carr and Wu [2002]. Second, we present a concrete procedure for implementing our scheme by applying it to plain vanilla options under exponential L?evy models. Finally, numerical examples in a model developed by Carr, Geman, Madan and Yor[2002] are used to demonstrate that our replication scheme is more efficient and more effective in practice than a standard static replication method.

Preliminary Results for Cooperative Extensions of the Bayesian Game

The descriptive theory of cooperative game with incomplete information developed to date is surveyed. The theory has the potential to provide game-theoretical foundations of economic analysis of the free societies in which organizations (coalitions) as corporations institute a non-market resource allocation mechanism while using the market resource allocation mechanism at the same time. The present-day corporations are interdependent, so the required game theory needs to model an environment in which the feasibility and implications of coordinated strategy choice within a coalition are influenced by the outsiders of strategy choice. The first part of the paper provides the key ingredients. After formulating the basic one-shot model, which synthesizes Harsanyi's Bayesian game and Aumann and Peleg's non-side-payment game (NTU game), and illustrating economic examples, two required conditions on an endogenously determined strategy are discussed: measurability with respect to an information structure, and Bayesian incentive compatibility. Several descriptive solution concepts that have been proposed to date are discussed. The second part addresses six issues studied in the literature: First, the existence of the descriptive solutions in the general setup. Second, explanation of information revelation, that is, a process through which private information turns into public information. Third, definitions of efficiency. Fourth, comparisons of several core concepts. Fifth, the existence results specific only to the Bayesian pure exchange economy, and revival of the core convergence theorem within the framework of the Bayesian pure exchange economy. Sixth, another view on coalition formation, specifically analyses of situations in which coalitional membership is anonymous.