A Fundamental Theorem of Asset Pricing for Large Financial Markets

We formulate the notion of “asymptotic free lunch” which is closely related to the condition “free lunch” of Kreps (1981) and allows us to state and prove a fairly general version of the fundamental theorem of asset pricing in the context of a large financial market as introduced by Kabanov and Kramkov (1994). In a large financial market one considers a sequence (Sⁿ)_n=1^∞ of stochastic stock price processes based on a sequence (Ωⁿ, Fⁿ, (F_tⁿ)_t∈In, Pⁿ)_n=1^∞ of filtered probability spaces. Under the assumption that for all n∈ N there exists an equivalent sigma‐martingale measure for Sⁿ, we prove that there exists a bicontiguous sequence of equivalent sigma‐martingale measures if and only if there is no asymptotic free lunch (Theorem 1.1). Moreover we present an example showing that it is not possible to improve Theorem 1.1 by replacing “no asymptotic free lunch” by some weaker condition such as “no asymptotic free lunch with bounded” or “vanishing risk.”     

Universal Portfolios

We exhibit an algorithm for portfolio selection that asymptotically outperforms the best stock in the market. Let x_i= (x_i, x_i2,…, x_im)^t denote the performance of the stock market on day i, where x_ii is the factor by which the jth stock increases on day i. Let b_i= (_bi1 b_i2, b_im)^t, b;_ij? 0, b_ij= 1, denote the proportion b_ij of wealth invested in the j th stock on day i. Then S_n= II_iⁿ= bi^tx_i is the factor by which wealth is increased in n trading days. Consider as a goal the wealth S_n*= max_b II_iⁿ=₁ b^tx_i that can be achieved by the best constant rebalanced portfolio chosen after the stock outcomes are revealed. It can be shown that Sn * exceeds the best stock, the Dow Jones average, and the value line index at time n. In fact, S_n* usually exceeds these quantities by an exponential factor. Let x₁, x₂, be an arbitrary sequence of market vectors. It will be shown that the nonanticipating sequence of portfolios db yields wealth such that , for every bounded sequence x₁, x₂…, and, under mild conditions, achieve where J, is an (m - 1) x (m - I) sensitivity matrix. Thus this portfolio strategy has the same exponential rate of growth as the apparently unachievable S*_n.     

On the rate of convergence of binomial Greeks

This study investigates the convergence patterns and the rates of convergence of binomial Greeks for the CRR model and several smooth price convergence models in the literature, including the binomial Black–Scholes (BBS) model of Broadie M and Detemple J ( 1996 ), the flexible binomial model (FB) of Tian YS ( 1999 ), the smoothed payoff (SPF) approach of Heston S and Zhou G ( 2000 ), the GCRR‐XPC models of Chung SL and Shih PT ( 2007 ), the modified FB‐XPC model, and the modified GCRR‐FT model. We prove that the rate of convergence of the CRR model for computing deltas and gammas is of order O(1/n), with a quadratic error term relating to the position of the final nodes around the strike price. Moreover, most smooth price convergence models generate deltas and gammas with monotonic and smooth convergence with order O(1/n). Thus, one can apply an extrapolation formula to enhance their accuracy. The numerical results show that placing the strike price at the center of the tree seems to enhance the accuracy substantially. Among all the binomial models considered in this study, the FB‐XPC and the GCRR‐XPC model with a two‐point extrapolation are the most efficient methods to compute Greeks. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark     

Data Warehousing and the Internet

Abstract

The technologies of the Internet and data warehousing are converging. This paper explores the synergies of these two revolutionary technologies. The strategic importance of data warehousing is presented through an examination of the applicable technology, growth of the market, and the factors encouraging that growth. The convergence of data warehousing technology and the Internet is discussed and strategic implications for modern businesses are addressed.     

CONVERGENCE OF BARRIER OPTION PRICES IN THE BINOMIAL MODEL

In this paper, we study the rate of convergence of the European barrier call option price given by the CRR binomial model to the Black–Scholes price as the number of periods n tends to infinity. In general the error is of order and we give explicit formulas for the coefficients of and 1/n in the asymptotic expansion of the error. These coefficients depend on the positions of the barrier and strike in the binomial lattice and enable us to give a rigorous explanation of the observed fact that the error is of order 1/n when n is chosen in an appropriate way.     

Responsibility of the University in Employability: Development and validation of a measurement scale across five studies

This paper develops and validates, at a confirmatory level, a second‐order scale to measure Responsibility of the University in Employability (RUE). First, the literature on the components of RUE is explored and a formative conceptual model is proposed to underpin its measurement using extant research in the field of organisational responsibility and employability. At the empirical level, the second‐order RUE model considers the reputation of the university, the teaching staff, and the matching activities with employers as components of RUE. This model is based on five empirical studies. The first is a small‐sample study based on the opinions of experts (n = 5) and the rest are based on representative samples of university students (n = 816, n = 1,082, n = 1,088, and n = 1,203). A very good fit between model and data were revealed (CFI = 0.975; RMSEA = 0.039; standardised X² = 2.676). The results indicate that matching activities with employers and teaching staff generate more RUE than university reputation. Guidelines are offered for managing the responsibility of the university in employability.     

Equilibrium solutions for resource dilemmas

Considered in this article is a class of resource dilemma games designed to study interactive decision behavior in the face of both strategic and environmental uncertainty. Groups of n members are asked to share a common resource pool whose exact size, x, is not known. Rather, x is sampled randomly from a uniform probability distribution which is common knowledge. Each group member j(j=1,...,n) requests r _j units from the random resource pool. Individual decisions are made independently and anonymously. Preplay communication is prohibited. If (r ₁+r ₂+...+r _n ) x, each member j is granted his/her request; otherwise, group members get nothing. We derive the Nash equilibrium solution for this resource dilemma game, and compare it to an expected utility model originally proposed by Suleiman and Rapoport (1988). We then show that the equilibrium solution accounts for the major qualitative features of experimental results reported in two previous studies.     

If only consumers knew: How sampling impacts wine innovation diffusion in the U.S. foodservice industry

A survey (n = 151) explored consumers’ experiences with wine-on-tap, a current trend in the U.S. foodservice industry. Wine consumers’ innovativeness (R² = .49) was explained by wine involvement, opinion leadership, and usage of information sources. Those who recently tried wine-on-tap (n = 43) were significantly more innovative (innovators) than those who never tried it (noninnovators). Furthermore, noninnovators expected to pay significantly less for a glass of wine-on-tap when compared with wine poured from a bottle. Contrary to expectations, the driving force for noninnovative behavior is lack of availability and awareness as opposed to a lack of interest in wine-on-tap.     

Absolute and Conditional Convergence in Both Zones of Cyprus: Statistical Convergence and Insitutional Divergence

This paper implements a time series econometric model to determine the timing of full convergence of incomes and output per capita and total factor productivity in the North and South of Cyprus, regardless of whether there is a political settlement or not. A significant dimension of the paper is its emphasis on institutional convergence, going beyond econometric or statistical convergence. Our results reveal that North Cyprus needs 17 years to catch up to full per capita income convergence, 16 years for per capita output convergence and 17 years for full total factor productivity (technological) convergence. The time‐series findings demonstrate that statistical convergence is occurring quite rapidly as the North is catching up to the average income and productivity levels of the South, which may confirm evidence of unconditional (beta) or absolute convergence, but there are significant differences between North and South in savings, tastes, population growth and technology. Most significantly, there are institutional differences highlighted in the study with a Two‐sector model of gate‐keeping and rent‐seeking which validates the premises of conditional convergence. Put differently, there are strong forces of divergence hidden behind our statistical findings.     

BLACK–SCHOLES REPRESENTATION FOR ASIAN OPTIONS

Asian options are securities with a payoff that depends on the average of the underlying stock price over a certain time interval. We identify three natural assets that appear in pricing of the Asian options, namely a stock S, a zero coupon bond B^T with maturity T, and an abstract asset A (an “average asset”) that pays off a weighted average of the stock price number of units of a dollar at time T. It turns out that each of these assets has its own martingale measure, allowing us to obtain Black–Scholes type formulas for the fixed strike and the floating strike Asian options. The model independent formulas are analogous to the Black–Scholes formula for the plain vanilla options; they are expressed in terms of probabilities under the corresponding martingale measures that the Asian option will end up in the money. Computation of these probabilities is relevant for hedging. In contrast to the plain vanilla options, the probabilities for the Asian options do not admit a simple closed form solution. However, we show that it is possible to obtain the numerical values in the geometric Brownian motion model efficiently, either by solving a partial differential equation numerically, or by computing the Laplace transform. Models with stochastic volatility or pure jump models can be also priced within the Black–Scholes framework for the Asian options.     

STABILITY OF THE EXPONENTIAL UTILITY MAXIMIZATION PROBLEM WITH RESPECT TO PREFERENCES

This paper studies stability of the exponential utility maximization when there are small variations on agent's utility function. Two settings are considered. First, in a general semimartingale model where random endowments are present, a sequence of utilities defined on converges to the exponential utility. Under a uniform condition on their marginal utilities, convergence of value functions, optimal payoffs, and optimal investment strategies are obtained, their rate of convergence is also determined. Stability of utility‐based pricing is studied as an application. Second, a sequence of utilities defined on converges to the exponential utility after shifting and scaling. Their associated optimal strategies, after appropriate scaling, converge to the optimal strategy for the exponential hedging problem. This complements Theorem 3.2 in [Nutz, M. (2012): Risk aversion asymptotics for power utility maximization. Probab. Theory & Relat. Fields 152, 703–749], which establishes the convergence for a sequence of power utilities.     

Convergence of optimal expected utility for a sequence of discrete‐time markets

We examine Kreps' conjecture that optimal expected utility in the classic Black–Scholes–Merton (BSM) economy is the limit of optimal expected utility for a sequence of discrete‐time economies that “approach” the BSM economy in a natural sense: The nth discrete‐time economy is generated by a scaled n‐step random walk, based on an unscaled random variable ζ with mean 0, variance 1, and bounded support. We confirm Kreps' conjecture if the consumer's utility function U has asymptotic elasticity strictly less than one, and we provide a counterexample to the conjecture for a utility function U with asymptotic elasticity equal to 1, for ζ such that .     

Estimating Arbitrator's Hidden Judgement in Final Offer Arbitration

In Final Offer Arbitration the arbitrator has to choose between two prices – salary offer a and demand b, presented by two negotiating sides. This situation is common e.g., in Major League Baseball since 1974, for players with at least three years experience. We model the arbitrator's decision process as follows. First, the arbitrator chooses an appropriate sum Z. Then he selects the one among a and b which is closer to the ‘proper sum’Z. The final amount selected is Y . Based on the history of n cases, the information available is the triplets {(Y _i, a _i, b _i) : i= 1, 2, . . . n}(the {Z _i} are hidden). It is assumed that the {Z _i} are random variables with a distribution which depends on an unknown parameter q and the challenge is to estimate q. Furthermore, since each case had different merits and characteristics, the resulting distribution is case-specific. Thus, our model allows the inclusion of explanatory variables. The statistical algorithm which we shall use is the Expectation-Maximization(EM) algorithm. In the paper, the statistical model is introduced in detail and the application of the EM algorithm to the available data is explained. Two numerical examples illustrate the use of the EM algorithm in estimating the arbitrator's hidden judgements.     

BEHAVIORAL PORTFOLIO SELECTION: ASYMPTOTICS AND STABILITY ALONG A SEQUENCE OF MODELS

We consider a sequence of financial markets that converges weakly in a suitable sense and maximize a behavioral preference functional in each market. For expected concave utilities, it is well known that the maximal expected utilities and the corresponding final positions converge to the corresponding quantities in the limit model. We prove similar results for nonconcave utilities and distorted expectations as employed in behavioral finance, and we illustrate by a counterexample that these results require a stronger notion of convergence of the underlying models compared to the concave utility maximization. We use the results to analyze the stability of behavioral portfolio selection problems and to provide numerically tractable methods to solve such problems in complete continuous‐time models.     

MODEL‐INDEPENDENT LOWER BOUND ON VARIANCE SWAPS

It is well known that, under a continuity assumption on the price of a stock S, the realized variance of S for maturity T can be replicated by a portfolio of calls and puts maturing at T. This paper assumes that call prices on S maturing at T are known for all strikes but makes no continuity assumptions on S. We derive semiexplicit expressions for the supremum lower bound on the hedged payoff, at maturity T, of a long position in the realized variance of S. Equivalently, is the supremum strike K such that an investor with a long position in a variance swap with strike K can ensure a nonnegative payoff at T. We study examples with constant implied volatilities and with a volatility skew. In our examples, is close to the fair variance strike obtained under the continuity assumption.     

Convergence in global markets and consumer behaviour

Consumer behavioural scientists such as economists and marketing researchers are interested in the degree to which global convergence is occurring with respect to various consumer behaviour dimensions, particularly the extent that consumption patterns in products appear to evolve and become more similar across different parts of the world. With increasing internationalization and cultural cross‐fertilization, the traditional societies of the world are converging in many ways. The strategic marketing of flavoured alcoholic beverages is a particularly interesting example of this evolutionary process to convergence. Consumers in countries of different cultural originations are developing preferences for the same products and show increasing sign of converging around global product identity. This article presents the results of a study analysing the evolutionary process.     

A document analysis of drowning prevention education resources in the United States

There have been long-standing calls to better educate the public at large on risks of drowning; yet limited evaluation has taken place on current resources in circulation. The purpose of this qualitative research is to develop an understanding of the content in currently circulated drowning prevention resources in the United States. Data points (n = 451) consisting of specific content within 25 different drowning prevention educational resources were analyzed using document analysis methods; a grounded theory approach was employed to allow for categorical development and indexing of the data. Results revealed six emerging categories, including safety precautions (n = 152), supervision (n = 109), preventing access (n = 57), safety equipment (n = 46), emergency procedures (n = 46), and aquatic education (n = 41). Results provide an initial insight into the composition of drowning prevention resources in the United States and provide a foundation for future research.     

Patterns of Research Productivity in the Business Ethics Literature: Insights from Analyses of Bibliometric Distributions

In any academic discipline, published articles in respective journals represent “production units” of scientific knowledge, and bibliometric distributions reflect the patterns in such outputs across authors or “producers.” Closely following the analysis approach used for similar studies in the economics and finance literature, we present the first study to examine whether there exists an empirical regularity in the bibliometric patterns of research productivity in the business ethics literature. Our results present strong evidence that there indeed exists a distinct empirical regularity. It is the so-called Generalized Lotka’s Law of scientific productivity pattern: the number of authors publishing n papers is about 1/n ^c of those publishing one paper. We discuss the likely processes that underlie the productivity pattern postulated by the Generalized Lotka’s Law. We find that the value of the exponent c is equal to about 2.6 for the comprehensive bibliometric data across the two leading business ethics journals. The observed research productivity pattern in the business ethics area, a relatively young discipline, is interestingly very consistent with those found in much older, related business disciplines like economics, accounting, and finance. We discuss the general implications of our findings.     

CONVERGENCE OF A LEAST‐SQUARES MONTE CARLO ALGORITHM FOR AMERICAN OPTION PRICING WITH DEPENDENT SAMPLE DATA

We analyze the convergence of the Longstaff–Schwartz algorithm relying on only a single set of independent Monte Carlo sample paths that is repeatedly reused for all exercise time‐steps. We prove new estimates on the stochastic component of the error of this algorithm whenever the approximation architecture is any uniformly bounded set of L² functions of finite Vapnik–Chervonenkis dimension (VC‐dimension), but in particular need not necessarily be either convex or closed. We also establish new overall error estimates, incorporating bounds on the approximation error as well, for certain nonlinear, nonconvex sets of neural networks.