ON ARBITRAGE AND DUALITY UNDER MODEL UNCERTAINTY AND PORTFOLIO CONSTRAINTS

We consider the fundamental theorem of asset pricing (FTAP) and the hedging prices of options under nondominated model uncertainty and portfolio constraints in discrete time. We first show that no arbitrage holds if and only if there exists some family of probability measures such that any admissible portfolio value process is a local super‐martingale under these measures. We also get the nondominated optional decomposition with constraints. From this decomposition, we obtain the duality of the super‐hedging prices of European options, as well as the sub‐ and super‐hedging prices of American options. Finally, we get the FTAP and the duality of super‐hedging prices in a market where stocks are traded dynamically and options are traded statically.     

A NOTE ON IS-LM AND STOCK ADJUSTMENT PROCESSES

A discrete-time model of a closed economy is employed in order to introduce the whole dynamics of stock adjustments in the IS-LM diagram. Discrete-time modeling allows us to represent the traverse process from the initial stationary state equilibrium to the new one by means of a family of intermediary IS(t) and LM(t) curves intersecting at each t to determine the appropriate short run equilibrium. Sufficient conditions for the dynamic process to be non-cyclical are derived under plausible assumptions. Two appendices provide the stability analysis and a numerical simulation of the model used.     

SOME REMARKS ON ARBITRAGE AND PREFERENCES IN SECURITIES MARKET MODELS

We introduce the notion of a market-free-lunch that depends on the preferences of all agents participating in the market. In semimartingale models of securities markets, we characterize no arbitrage (NA) and no-free-lunch-with-vanishing-risk (NFLVR) in terms of the market-free-lunch and show that the difference between NA and NFLVR consists in the selection of the class of monotone, respectively monotone and continuous, utility functions that determines the absence of the market-free-lunch. We also provide a direct proof of the equivalence between the absence of a market-free-lunch, with respect to monotone concave preferences, and the existence of an equivalent (local/sigma) martingale measure.     

A NOTE ON SEMIVARIANCE

In a recent paper ( Jin, Yan, and Zhou 2005 ), it is proved that efficient strategies of the continuous-time mean–semivariance portfolio selection model are in general never achieved save for a trivial case. In this note, we show that the mean–semivariance efficient strategies in a single period are always attained irrespective of the market condition or the security return distribution. Further, for the below-target semivariance model the attainability is established under the arbitrage-free condition. Finally, we extend the results to problems with general downside risk measures.     

A NOTE ON MAIL SURVEYS AND RESPONSE RATES IN LOGISTICS RESEARCH

Logistics researchers frequently use mail surveys to collect data. This paper documents the decline in response rates to surveys reported in JBL, and presents a content analysis of mail survey results reported in two leading logistics journals, the Journal of Business Logistics and the International Journal of Physical Distribution and Logistic Management. One interesting finding is the more questionnaires mailed out in a given study, the lower the response rate.     

ARBITRAGE AND INFORMATION IN A SEQUENTIAL ECONOMY WITH MANY CREDIT AGENCIES

This paper augments the theoretical foundations of organized commodity futures markets and uncovers singular facts about arbitrage and the role of information. Using the term "credit agency" to embrace organized futures markets such as the Chicago Board of Trade as well as independent brokerage houses, we extend the extant theory of temporary equilibrium for an economy with a single credit agency to economies with many credit agencies. In the process, we find that arbitrage with no risk of bankruptcy and with perfect interagency trade information can be incompatible with equilibrium (exact or approximate). On the other hand, the usual regularity assumptions are sufficient for the existence of at least an approximate equilibrium, provided that interagency trade information is imperfect (or risky). However, such imperfect information limits arbitrage so different agencies can have different prices.     

A NOTE ON THE QUANTILE FORMULATION

Many investment models in discrete or continuous‐time settings boil down to maximizing an objective of the quantile function of the decision variable. This quantile optimization problem is known as the quantile formulation of the original investment problem. Under certain monotonicity assumptions, several schemes to solve such quantile optimization problems have been proposed in the literature. In this paper, we propose a change‐of‐variable and relaxation method to solve the quantile optimization problems without using the calculus of variations or making any monotonicity assumptions. The method is demonstrated through a portfolio choice problem under rank‐dependent utility theory (RDUT). We show that this problem is equivalent to a classical Merton's portfolio choice problem under expected utility theory with the same utility function but a different pricing kernel explicitly determined by the given pricing kernel and probability weighting function. With this result, the feasibility, well‐posedness, attainability, and uniqueness issues for the portfolio choice problem under RDUT are solved. It is also shown that solving functional optimization problems may reduce to solving probabilistic optimization problems. The method is applicable to general models with law‐invariant preference measures including portfolio choice models under cumulative prospect theory (CPT) or RDUT, Yaari's dual model, Lopes' SP/A model, and optimal stopping models under CPT or RDUT.     

A NOTE ON T. H. HUXLEY AND THE SOCIETY OF ARTS

T. H. Huxley's wide-ranging scientific and educational interests included support for home economics in the new 1870 school system. Part of this interest was expressed in his attendance at the first Domestic Economy Congress of the Society of Arts in 1877, itself prominent in supporting reform in housing, health and education.     

ON THE LOWER ARBITRAGE BOUND OF AMERICAN CONTINGENT CLAIMS

We prove that in a discrete‐time market model the lower arbitrage bound of an American contingent claim is itself an arbitrage‐free price if and only if it corresponds to the price of the claim optimally exercised under some equivalent martingale measure.     

MARKETS AND GAMES: A SIMPLE EQUIVALENCE AMONG THE CORE,EQUILIBRIUM AND LIMITED ARBITRAGE

This note provides simple proofs of the equivalence among the core, equilibrium and limited arbitrage in markets with short sales, and with uniform strictly convex preferences.     

A NOTE ON METROECONOMICA: SHACKLE'S CONTRIBUTION

In the 1950s Shackle contributed a number of important articles to Metroeconomica, a new economic journal founded by Eraldo Fossati in 1949 and published in Trieste (Italy). The journal gave considerable prominence to Shackle's theory of decision under uncertainty through publication of many articles, but, above all, through publication of the proceedings of a symposium held in 1959 and entitled ‘Shackle's theory on decision’. The aim of this note is to clarify why Metroeconomica gave particular importance to Shackle's perspective.     

A NOTE ON THE GENERALIZED MULTIBETA CAPM

The unified beta theory of Connor (1984) requires that the market portfolio be well diversified in a given factor structure. Wei (1988) extended Connor's results without relying on this assumption. This note provides an alternative to Wei's result by assuming that residuals from the projection of asset return on a set of k factors follow a joint elliptical distribution.     

DOMAIN RESTRICTIONS ON INTEREST RATES IMPLIED BY NO ARBITRAGE

This paper derives domain restrictions on interest rates implied by no‐arbitrage. These restrictions are important for the study of arbitrage opportunities on bond markets, for regulation of these markets, and for econometric modelling.     

A NOTE ON THE EFFECTS OF TAXES ON OPTIMAL INVESTMENT

We integrate two approaches to portfolio management problems: that of Morton and Pliska (1995) for a portfolio with risky and riskless assets under transaction costs, and that of Cadenillas and Pliska (1999) for a portfolio with a risky asset under taxes and transaction costs. In particular, we show that the two surprising results of the latter paper, results shown for a taxable market consisting of only a single security, extend to a financial market with one risky asset and one bond: it can be optimal to realize not only losses but also gains, and sometimes the investor prefers a positive tax rate.