股市有免费午餐吗——一个基于随机过程的理论分析

关于股市是否存在免费午餐,理论存在着截然不同的观点。一些经济学家依据有效市场假说,认为天下没有免费的午餐。然而,近年来人们逐渐认识到,在有关金融市场的理论模型中,某些形式巧妙的免费午餐是可以得到的。这一结果与基本的经济学原理相冲突,一些经济学家对解释这一有趣的问题做出了努力。本文从股票回报率随机波动的假设出发,利用伊滕定理,在关于投资组合回报率大于政府债券回报率的概率计算基础上,推导出股市存在免费午餐的条件,并对每一因素进行了分析和概率计算。在此基础上,对投资者提出了理性投资建议。     

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.”     

Malliavin's Calculus in Insider Models: Additional Utility and Free Lunches

We consider simple models of financial markets with regular traders and insiders possessing some extra information hidden in a random variable that is accessible to the regular trader only at the end of the trading interval. The problems we focus on are the calculation of the additional utility of the insider and a study of his free lunch possibilities. The information drift—that is, the drift to eliminate in order to preserve the martingale property in the insider's filtration—turns out to be the crucial quantity needed to answer these questions. It is most elegantly described by the logarithmic Malliavin trace of the conditional laws of the insider information with respect to the filtration of the regular trader. Several examples are given to illustrate additional utility and free lunch possibilities. In particular, if the insider has advance knowledge of the maximal stock price process, given by a regular diffusion, arbitrage opportunities exist.     

ARBITRAGE AND FREE LUNCH WITH BOUNDED RISK FOR UNBOUNDED CONTINUOUS PROCESSES

We give two examples showing that for unbounded continuous price processes, the no-free-lunch assumption and the existence of an equivalent martingale measure are not equivalent. In fact it turns out that the notion of an equivalent local martingale measure is natural in this context.     

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.     

DO ARBITRAGE‐FREE PRICES COME FROM UTILITY MAXIMIZATION?

In this paper we ask whether, given a stock market and an illiquid derivative, there exists arbitrage‐free prices at which a utility‐maximizing agent would always want to buy the derivative, irrespectively of his own initial endowment of derivatives and cash. We prove that this is false for any given investor if one considers all initial endowments with finite utility, and that it can instead be true if one restricts to the endowments in the interior. We show, however, how the endowments on the boundary can give rise to very odd phenomena; for example, an investor with such an endowment would choose not to trade in the derivative even at prices arbitrarily close to some arbitrage price.     

On the Existence of Minimax Martingale Measures

Embedding asset pricing in a utility maximization framework leads naturally to the concept of minimax martingale measures. We consider a market model where the price process is assumed to be an ^d‐semimartingale X and the set of trading strategies consists of all predictable, X‐integrable, ^d‐valued processes H for which the stochastic integral (H.X) is uniformly bounded from below. When the market is free of arbitrage, we show that a sufficient condition for the existence of the minimax measure is that the utility function u : → is concave and nondecreasing. We also show the equivalence between the no free lunch with vanishing risk condition, the existence of a separating measure, and a properly defined notion of viability.     

MARTINGALE MEASURES FOR DISCRETE-TIME PROCESSES WITH INFINITE HORIZON

Let ( S_t ) _tεI be an R^d-valued adapted stochastic process on (Ω, , ( _t ) _tεI , P ). A basic problem occurring notably in the analysis of securities markets, is to decide whether there is a probability measure Q on  equivalent to P such that ( S_t ) _tεI is a martingale with respect to Q. It is known (see the fundamental papers of Harrison and Kreps 1979; Harrison and Pliska 1981; and Kreps 1981) that there is an intimate relation of this problem with the notions of "no arbitrage" and "no free lunch" in financial economics. We introduce the intermediate concept of "no free lunch with bounded risk." This is a somewhat more precise version of the notion of "no free lunch." It requires an absolute bound of the maximal loss occurring in the trading strategies considered in the definition of "no free lunch." We give an argument as to why the condition of "no free lunch with bounded risk" should be satisfied by a reasonable model of the price process ( S_t ) _tεI of a securities market. We can establish the equivalence of the condition of "no free lunch with bounded risk" with the existence of an equivalent martingale measure in the case when the index set I is discrete but (possibly) infinite. A similar theorem was recently obtained by Delbaen (1992) for continuous-time processes with continuous paths. We can combine these two theorems to get a similar result for the continuous-time case when the process ( S_t ) _{t εR+} is bounded and, roughly speaking, the jumps occur at predictable times. In the infinite horizon setting, the price process has to be "almost a martingale" in order to allow an equivalent martingale measure.     

The workplace lunch room: an arena for multicultural eating

Many countries in Europe have experienced growing migration since World War II. It is estimated that more than one in five Swedes living today has roots in other countries and cultures. Segregation in terms of ethnic origin in housing areas makes it easier to maintain the language and cultural traditions of the home country when it comes to cooking and eating. In extremely segregated housing areas, there may even be no interface between foreign cultural traditions and Swedish traditions in food consumption. Almost every inhabitant in the age range 20–65 years spends a number of years in workplaces outside the home. Workplaces are generally melting pots for employees of all ages and ethnic groups. In this study, a bus company lunch room served as a field for studying preferences in food, meals structure and eating patterns during lunch breaks. The city centre lunch room was visited by every driver at least once during their working day for coffee/tea, lunch or a rest. The lunch room served as an arena for discussions and exposure to new foods customs relating to meals and eating. It thus constituted a place for cultural exchange about food preferences and for forming opinions about individuals and nationalities, including Swedes. The methods for gathering empirical material for the analysis were participant observations and semi‐structured interviews. Food consumption can be recognized as a marker of class and status in the same way as consumption of leisure activities and clothing. Some new criteria in identifying members of we‐groups in relation to others can be added to the classical criteria. When language fails in communication, visible signs become more important. A workplace lunch room is a clear arena for attitude formation. Attitudes may be conservative or stereotyped but sometimes evoke the curiosity to eat something different. In a multicultural arena such as a workplace lunch room, the knowledge available about food, meals and preferences is sometimes far from the real truth, especially when visible impressions are not followed by verbal communication, which can sometimes lead to incomplete and narrow‐minded conclusions.     

Parental perception of lunch schemes in Danish kindergartens: A cross-sectional survey

Children’s daily consumption of food in childcare institutions has an impact on their public health nutritional status. The collaboration of parents and employees of kindergartens is important to ensure healthy eating habits among the next generation. Consequently, evaluations of lunch schemes are important to provide a good foundation for enhancing communication between home and institutional settings. The aim of this article is to assess parental satisfaction and identify themes related to parental perceptions of lunch schemes in Danish kindergartens. A survey was developed and distributed in four kindergartens with lunch schemes. A combination of closed and open questions were used to evaluate satisfaction and identify positive and negative aspects of the lunch schemes. Parents of 93 children participated in the study and the response rate was 55%. Eighty-nine percent expressed satisfaction with their children’s lunch scheme. According to parents, the most positive aspects were that lunch schemes serve a variety of food, their ability to prevent neophobia, that children learn that eating is a social occasion, and that the arrangements offer convenience to parents. The negative aspects identified were the lack of communication between the kindergarten childcare institutions and the parents regarding the food. Overall, parents are very satisfied with their children’s lunch schemes; however, the information between institutions and parents could be improved.     

Martingale Measures For A Class of Right-Continuous Processes

The subject of the present paper is the following. Suppose that W is a class of adapted, right-continuous processes on the continuous time horizon [0, 1], and for every stopping time and W , () is bounded below. A necessary and sufficient condition will be given for the existence of a probability measure Q which is equivalent to the original measure and such that each process in W is a martingale under Q . If the processes in W represent the discounted prices of available securities, then the condition given here for the existence of a martingale measure can be interpreted as absence of "free lunch" in the securities market. This is a familiar kind of theorem from the finance literature; the novelty of this paper is that the security prices are not required to be in LP for some 1 p , nor are they assumed to be continuous. Also, the concept of free lunch is invariant under the substitution of the original probability measure by an equivalent probability measure. the assumption that () is bounded below for every W and stopping time is quite natural since prices are nonnegative.
We shall define a class of admissible subjective probability measures and assume that each agent in the economy has selected a subjective probability measure from (hat class. Subjective free lunch for an agent will be defined using his or her subjective probability measure. It will be shown that under an additional condition the existence of free lunch is equivalent to the existence of a common subjective free lunch simultaneously for all possible agents in the economy.     

自由贸易与贸易保护主义——公平与效率问题

当今世界 ,贸易自由化成为世界经济发展的主流 ,降低关税和非关税壁垒成为各国双边和多边谈判的主要议题。自由贸易与贸易保护主义的争论由来已久 ,自由贸易的效率以及产生的不公平问题用“补偿原则”来解决是存在局限性的 ,所以 ,自由贸易和贸易保护主义之间政策的权衡十分必要。解决贸易自由化中不公平的问题应从政府制定规则、完善社会保障和建立社会道德标准三方面加以着手。     

ASSET PRICE BUBBLES IN INCOMPLETE MARKETS*

This paper studies asset price bubbles in a continuous time model using the local martingale framework. Providing careful definitions of the asset's market and fundamental price, we characterize all possible price bubbles in an incomplete market satisfying the “no free lunch with vanishing risk (NFLVR)” and “no dominance” assumptions. We show that the two leading models for bubbles as either charges or as strict local martingales, respectively, are equivalent. We propose a new theory for bubble birth that involves a nontrivial modification of the classical martingale pricing framework. This modification involves the market exhibiting different local martingale measures across time—a possibility not previously explored within the classical theory. Finally, we investigate the pricing of derivative securities in the presence of asset price bubbles, and we show that: (i) European put options can have no bubbles; (ii) European call options and discounted forward prices have bubbles whose magnitudes are related to the asset's price bubble; (iii) with no dividends, American call options are not exercised early; (iv) European put‐call parity in market prices must always hold, regardless of bubbles; and (v) futures price bubbles can exist and they are independent of the underlying asset's price bubble. Many of these results stand in contrast to those of the classical theory. We propose, but do not implement, some new tests for the existence of asset price bubbles using derivative securities.     

ASSET PRICING WITH NO EXOGENOUS PROBABILITY MEASURE

In this paper, we propose a model of financial markets in which agents have limited ability to trade and no probability is given from the outset. In the absence of arbitrage opportunities, assets are priced according to a probability measure that lacks countable additivity. Despite finite additivity, we obtain an explicit representation of the expected value with respect to the pricing measure, based on some new results on finitely additive measures. From this representation we derive an exact decomposition of the risk premium as the sum of the correlation of returns with the market price of risk and an additional term, the purely finitely additive premium, related to the jumps of the return process. We also discuss the implications of the absence of free lunches .     

Viability and Equilibrium in Securities Markets with Frictions

In this paper we study some foundational issues in the theory of asset pricing with market frictions. We model market frictions by letting the set of marketed contingent claims (the opportunity set) be a convex set, and the pricing rule at which these claims are available be convex. This is the reduced form of multiperiod securities price models incorporating a large class of market frictions. It is said to be viable as a model of economic equilibrium if there exist price-taking maximizing agents who are happy with their initial endowment, given the opportunity set, and hence for whom supply equals demand. This is equivalent to the existence of a positive lineaar pricing rule on the entirespace of contingent claims—an underlying frictionless linear pricing rule—that lies below the convex pricing rule on the set of marketed claims. This is also equivalent to the absence of asymptotic free lunches—a generalization of opportunities of arbitrage. When a market for a nonmarketed contingent claim opens, a bid-ask price pair for this claim is said to be consistent if it is a bid-ask price pair in at least a viable economy with this extended opportunity set. If the set of marketed contingent claims is a convex cone and the pricing rule is convex and sublinear, we show that the set of consistent prices of a claim is a closed interval and is equal (up to its boundary) to the set of its prices for all the underlying frictionless pricing rules. We also show that there exists a unique extended consistent sublinear pricing rule—the supremum of the underlying frictionless linear pricing rules—for which the original equilibrium does not collapse when a new market opens, regardless of preferences and endowments. If the opportunity set is the reduced form of a multiperiod securities market model, we study the closedness of the interval of prices of a contingent claim for the underlying frictionless pricing rules.     

School lunch—Children’s space or teachers’ governmentality?

This article discusses social aspects of school lunches in Norway. How do 11‐year‐old students experience and perceive their packed lunches and lunch breaks and to what extent is the lunch break a space for children's sociality or an area for teachers’ governmentality? The study is based on 25 focus group discussions and drawing and writing assignments with 165 participants. A large proportion of the students expressed that they appreciated their packed lunches because they could decide for themselves what and how much to eat. Additionally, shortage of time and disturbance and noise in the classroom could ruin a good meal. The main issue that the students raised in relation to our question of sociality was with whom they could sit and eat their packed lunches. This finding underlines the importance of considering the emotional dimensions of eating and that commensal eating is not dependent on sharing the same food. The children experienced that the lunch break was governed by an adult agenda in which they had limited opportunities to create their own spaces.     

BETTER THAN DYNAMIC MEAN‐VARIANCE: TIME INCONSISTENCY AND FREE CASH FLOW STREAM

As the dynamic mean‐variance portfolio selection formulation does not satisfy the principle of optimality of dynamic programming, phenomena of time inconsistency occur, i.e., investors may have incentives to deviate from the precommitted optimal mean‐variance portfolio policy during the investment process under certain circumstances. By introducing the concept of time inconsistency in efficiency and defining the induced trade‐off, we further demonstrate in this paper that investors behave irrationally under the precommitted optimal mean‐variance portfolio policy when their wealth is above certain threshold during the investment process. By relaxing the self‐financing restriction to allow withdrawal of money out of the market, we develop a revised mean‐variance policy which dominates the precommitted optimal mean‐variance portfolio policy in the sense that, while the two achieve the same mean‐variance pair of the terminal wealth, the revised policy enables the investor to receive a free cash flow stream (FCFS) during the investment process. The analytical expressions of the probability of receiving FCFS and the expected value of FCFS are derived.     

CONVEX RISK MEASURES FOR GOOD DEAL BOUNDS

We study convex risk measures describing the upper and lower bounds of a good deal bound, which is a subinterval of a no‐arbitrage pricing bound. We call such a convex risk measure a good deal valuation and give a set of equivalent conditions for its existence in terms of market. A good deal valuation is characterized by several equivalent properties and in particular, we see that a convex risk measure is a good deal valuation only if it is given as a risk indifference price. An application to shortfall risk measure is given. In addition, we show that the no‐free‐lunch (NFL) condition is equivalent to the existence of a relevant convex risk measure, which is a good deal valuation. The relevance turns out to be a condition for a good deal valuation to be reasonable. Further, we investigate conditions under which any good deal valuation is relevant.     

Sollten Zentralbanken unabhängig sein? Ergänzungen zu Stefan Schäfer

This article extends the inspection of Central Bank Independence (CBI) with respect to inflation performance to an examination of the relationship between CBI and economic welfare in general. The common view of monetary neutrality, i.e. a “free lunch” of CBI with respect to economic growth and employment, is contested on the basis of neo- and post-Keynesian theories of policy interactions and market constellations. Nevertheless, the fact has to be taken seriously that there is a broad discussion under way about the merits of CBI. The defenders of CBI must be on the lookout against a broad political and scientific offensive against the cornerstones of “German stability culture”.     

Strategic currency hedging and global portfolio investments upside down

The literature on the convenience of currency hedging of international portfolio investments has not reached a final verdict. There are arguments for (Perold and Schulman [Perold, A.F. and Schulman, E.C. (1988). The free lunch in currency hedging: implications for investment policy and performance standards, Financial Analysts Journal, May/June Vol. 44, No. 3: 45-52]) and against (Froot [Froot, K. (1993). Currency hedging over long horizons. NBER Working Paper 4355.] and Campbell et al. [Campbell, J.Y., Viceira, L.M. and White, J.S. (2003). Foreign currency for long-term investors. The Economic Journal, Volume 113, Number 486, (March), pp. C1-C25(1)]). This paper analyzes the perspective of global investors based in emerging markets, for which hedging should imply increasing expected returns. The question thus is whether currency hedging is a “free lunch” in this case. No free lunch exists, as it turns out. Hard currencies act as natural hedges against global (and local) portfolio losses, since they tend to appreciate with respect to emerging market currencies when the world portfolio return is negative. Therefore, in this case currency hedging increases volatility—although also increasing expected returns. This result is likely to hold generally for relatively open economies with flexible exchange rate regimes.