Infinitely many securities and the fundamental theorem of asset pricing

Several authors have pointed out the possible absence of martingale measures for static arbitrage-free markets with an infinite number of available securities. This paper addresses this caveat by drawing on projective systems of probability measures. Firstly, it is shown that there are two distinct sorts of models whose treatment is necessarily different. Secondly, and more important, we analyze those situations for which one can provide a projective system of ó .additive measures whose projective limit may be interpreted as a risk-neutral probability. Hence, the Fundamental Theorem of Asset Pricing is extended so that it can apply for models with infinitely many assets.

ON THE FUTURE CONTRACT QUALITY OPTION: A NEW LOOK

The paper provide a new method to replicate and price the quality options usually embedded in many future contracts. The replicating strategies may draw on both the future contract and its related calls and puts. They also yield the quality option theoretical price in perfect markets, as well as upper and lower bounds for its bid or ask prices if frictions are incorporated. With respect to previous literature, this new approach seems to reflect four contributions: Firstly, the analysis does not depend on any dynamic assumption concerning the TSIR behaviour, secondly, it incorporates the information contained in calls and puts whose underlying security is the future contract, thirdly, it allows us to use real market perfectly synchronized prices, and fourthly, transaction costs can be considered. The paper presents an empirical test involving the German market that reveals some differences with regard to previous studies.

GENERALIZED VECTOR RISK FUNCTIONS

The paper introduces a new notion of vector-valued risk function. Both deviations and expectation bounded coherent risk measures are defined and analyzed. The relationships with both scalar and vector risk functions of previous literature are discussed, and it is pointed out that this new approach seems to appropriately integrate several preceding point of view. The framework of the study is the general setting of Banach lattices and Bochner integrable vector-valued random variables. Sub-gradient linked representation theorems, as well as portfolio choice problems, are also addressed, and general optimization methods are presented. Finally, practical examples are provided.

MARKET IMPERFECTIONS, DISCOUNT FACTORS AND STOCHASTIC DOMINANCE: AN EMPIRICAL ANALYSIS WITH OIL-LINKED DERIVATIVES

Oil-linked derivatives are becoming very important in Modern Investment Theory. Accordingly, the analysis of Pricing Techniques and Portfolio Choice Problems involving these securities is a major topic for both managers and researchers. We focus on both the No-Arbitrage Approach and Stochastic Discount Factor (SDF) based methods in order to study oil-linked derivatives available at The New York Mercantile Exchange, Inc, one of the world's largest markets in energy and precious metals. First, we generalize some theoretical properties of the SDF in order to capture the effects induced by the bid-ask spread when analyzing dominated/efficient portfolios. Secondly, we apply our findings and empirically analyze the existence of dominated assets and portfolios in the oil derivatives market. Our results reveal the systematic presence of dominated prices, which should be taken into account by traders when composing their portfolios. Additionally, the test yields pricing and portfolio choice methods as well as new strategies that may allow brokers to outperform their service for their clients. It is worth to point out that the conclusions of the test have two important characteristics: On the one hand, they are very precise since we draw on perfectly synchronized bid/ask prices, as provided by Reuters. On the other hand, they are robust in the sense that they do not depend on any assumption about the underlying asset price dynamics. Finally, despite the empirical test focuses on oil derivatives, the methodology is general enough to apply to a broad range of markets.

Hedging bond portfolios versus infinitely many ranked factors of risk

The paper considers bond portfolios affected by both interest-rate- and default-risk. In order to guarantee a correct performance of our analysis we will hedge against an infinite number of factors. Hence we do not have to impose and do not depend on any assumption concerning the dynamic behavior of the term structure of interest rates. On the other hand, since a complete hedging is not feasible unless some ideal situations hold, we rank the factors according to the empirical evidence. Thus, we make the most important risks vanish and we minimize the effect of those kinds of risk less usual in practice.

Optimal risk in marketing resource allocation

Marketing resource allocation is increasingly based on the optimization of expected returns on investment. If the investment is implemented in a large number of repetitive and relatively independent simple decisions, it is an acceptable method, but risk must be considered otherwise. The Markowitz classical mean-deviation approach to value marketing activities is of limited use when the probability distributions of the returns are asymmetric (a common case in marketing). In this paper we consider a unifying treatment for optimal marketing resource allocation and valuation of marketing investments in risky markets where returns can be asymmetric, using coherent risk measures recently developed in finance. We propose a set of first order conditions for the solution, and present a numerical algorithm for the computation of the optimal plan. We use this approach to design optimal advertisement investments in sales response managementResource allocation, Coherent risk measures, Optimization, Sales response models

On the future contract quality option: a new look

This article provides a new method for replicating and pricing the quality options usually embedded in many future contracts. The replicating strategies may draw on both the future contract as well as its related calls and puts. They also yield the quality option theoretical price in perfect markets, as well as upper and lower bounds for its bid or ask prices if frictions are incorporated. With respect to previous literature, this new approach seems to reflect five contributions: First, the analysis does not depend on any dynamic assumption concerning the Term Structure of Interest Rates (TSIR) behaviour; second, it incorporates the information contained in calls and puts on the future contract; third, it allows us to use real market perfectly synchronized prices; fourth, transaction costs can be considered and, finally, this article shows that the quality option may be a useful security in the portfolio of many traders. These traders will make the future contract more effective as a hedging instrument. This article also presents an empirical test involving the German market.