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

Duality theory and slackness conditions in multiobjective linear programming

AbstractThe aim of this paper is to develop a duality theory for linear multiobjective programming verifying similar properties as in the scalar case. We use the so-called “strongly proper optima” and we characterize such optima and its associated dual solutions by means of some complementary slackness conditions. Moreover, the dual solutions can measure the sensitivity of the primal optima

Constraining in situ cosmogenic nuclide paleo-production rates using sequential lava flows during a paleomagnetic field strength low

The geomagnetic field prevents a portion of incoming cosmic rays from reaching Earth’s atmosphere. During magnetic reversals and excursions, the field strength can decrease by up to 90% relative to the modern-day value. During such anomalies, cosmic ray bombardment to Earth’s atmosphere increases as evident from atmospheric ¹⁰Be anomalies recorded in sediment and ice cores. However, how the flux of cosmic rays to Earth’s surface varies during such geomagnetic anomalies is not well constrained. We measured fossil cosmogenic ³He in olivine from the tops of two pairs of ⁴⁰Ar/³⁹Ar age-dated Tahitian lava flows that erupted during the Matuyama-Brunhes reversal precursor event. We corrected these raw values for the diffusive loss of helium caused by heating from the overlying flow with a diffusion model using cooling rates and maximum temperature conditions based on field measurements of active lava flows from Kilauea, Hawaii. We assume the maximum temperature suggested by field measurements and thus present a limiting case for the highest diffusive loss corrections and thus the highest paleo-production rates. Based on paleomagnetic field strength reconstructions and scaling factor models, the upper limits of the corrected in situ 3He paleo-production rates (100 ± 23, 144 ± 35 atoms g⁻¹ a⁻¹) are in agreement with those expected during the period of a geomagnetic field strength low when these flow tops were exposed. However, the more plausible contact temperatures (<700°C maximum temperature in diffusion model) are associated with diffusion corrected paleo-production rates lower than those predicted by scalar models. This potential underestimation is likely a function of changes in local non-dipole field components, atmospheric density and/or an overestimation of the dipole field strength reduction during the M-B precursor event

Effect of Tai Chi Exercise Combined with Mental Imagery Theory in Improving Balance in a Diabetic and Elderly Population

BACKGROUND: One of the effects of diabetes mellitus (DM), peripheral neuropathy, affects the sensation in the feet and can increase the chance of falling. The purpose of the study was to investigate the effect of 8 weeks of Tai Chi (TC) training combined with mental imagery (MI) on improving balance in people with diabetes and an age matched control group.MATERIAL AND METHODS: Seventeen healthy subjects and 12 diabetic sedentary subjects ranging from 40–80 years of age were recruited. All subjects in both groups attended a Yang style of TC class using MI strategies, 2 sessions a week for 8 weeks. Each session was one hour long. Measures were taken using a balance platform test, an Activities-specific Balance Confidence (ABC) Scale, a one leg standing test (OLS), functional reach test (FRT) and hemoglobin A1C. These measures were taken twice, pre and post-study, for both groups.RESULTS: Both groups experienced significant improvements in ABC, OLS, FRT (P\u3c0.01) after completing 8 weeks of TC exercise with no significant improvement between groups. Subjects using the balance platform test demonstrated improvement in balance in all different tasks with no significant change between groups. There was no significant change in HbA1C for the diabetic group.CONCLUSIONS: All results showed an improvement in balance in the diabetic and the control groups; however, no significant difference between the groups was observed. Since the DM group had more problems with balance impairment at baseline than the control, the diabetic group showed the most benefit from the TC exercise