Arbitrary Preferences Research Articles

Equilibrium population dynamics when mating is by mutual choice based on age

We consider a steady state model of mutual mate choice in which an individual’s mate preferences depend on his/her age, and the preferences are over the ages of prospective mates of the opposite sex. We present a discrete time (and age) model corresponding to successive mating seasons. Males are fertile for m periods (corresponding to ‘age’ i=1 to m) and females for n≤m periods (they have ages j=1 to n), which is all that distinguishes the sexes. Although we can deal with arbitrary preferences, we concentrate on a simple fertility model where the common utility to a male age i and female age j who mate is the number K=min(m−i+1,n−j+1) of future periods of joint fertility. The incoming sex ratio R of age 1 males to age 1 females is given exogenously. In each period individuals are randomly (non assortatively) matched and form a mated couple by mutual consent; otherwise they go into the next period unmated and older. We derive properties of equilibrium threshold acceptance strategies and establish the existence of time-invariant age distributions. Our methods determine the age distribution of couples at marriage (mating) and the population sex ratio (OSR) at equilibrium. Since this can be determined empirically in a population, our model can be used to rule out most systems of age preferences (those not consistent with the observed distribution). This extends earlier models of mutual choice with one dimensional types of Alpern and Reyniers [1999. Strategic mating with homotypic preferences. J. Theor. Biol. 198, 71–88; 2005. Strategic mating with common preferences. J. Theor. Biol. 237, 337–354] where individuals sought, respectively, individuals with similar or high types, but in those models an individual’s type was fixed over time.Under the simple fertility model, at equilibrium the maximum age of an acceptable partner is increasing in the age of the searcher. Our results relate to discussions in the literature regarding optimal parental age differences, age-related mate preferences, and to mate choice in general. We believe our model will be used as a tool in future investigations in these areas.

Optimal Liquidity Provision in Limit Order Markets

A small investor provides liquidity at the best bid and ask prices of a limit order market. For small spreads and frequent orders of other market participants, we explicitly determine the investor's optimal policy and welfare. In doing so, we allow for general dynamics of the mid price, the spread, and the order flow, as well as for arbitrary preferences of the liquidity provider under consideration.

Forward Indifference Valuation of American Options

We analyze the American option valuation problem with the forward performance criterion introduced by Musiela and Zariphopoulou (2008). In this framework, utility evolves forward in time without reference to a specific future time horizon. Moreover, risk preferences change with stochastic market conditions, which is natural as investors are clearly more risk averse in economic downtimes. We examine two applications: the valuation of American options with stochastic volatility and the modeling of early exercises of American-style employee stock options. Finally, we introduce the marginal forward performance price introduced by Davis (1997). Among others, we find that, for arbitrary preferences, the marginal forward indifference price is always independent of the investor's wealth and is represented as the claim's risk-neutral price under the minimal martingale measure.

INFORMATION AND THE EQUITY PREMIUM

We determine how better information affects the average equity premium in a standard representative-agent exchange economy. Perfect information obviously eliminates the equity premium, and a particular kind of information about the level of future consumption always lowers the average equity premium. Surprisingly, information sometimes raises the average equity premium, no matter what the preferences of the representative agent. Information purely about the volatility either of consumption or the marginal utility of consumption raises the equity premium for a wide class of preferences. Moreover, information can raise the average equity premium by an arbitrarily large percentage (while still matching important magnitudes, such as average growth and the risk-free rate). We consider two different economies: a two-period economy with arbitrary preferences for the representative agent; and an infinite horizon economy, in which we restrict both preferences and the endowment distribution.

Erratum

There is an error in my 2004 paper “Wealth, Information Acquisition and Portfolio Choice”. This note shows how to correct it by adjusting the hypotheses of the model. Specifically, it assumes that agents learn about the stock’s mean payoff rather than about its realization. All the conclusions of the paper remain valid. There is a mistake in the derivation of agents’ unconditional expected utility in “Wealth, Information Acquisition and Portfolio Choice” (Review of Financial Studies, 17(3) (2004), pages 879-914). Some formulas need to be corrected and some assumptions adjusted, but all the conclusions of the paper remain valid. In particular, it remains the case that wealthier investors collect more information and that, as a result, they hold a larger fraction of their wealth in stocks even though their relative risk aversion is not lower. The unconditional expected utility is approximated using a Taylor series expansion, in which higher order terms are dropped. In fact, these terms cannot be neglected under the payoff structure postulated in the paper. As a result, the demand for information cannot be evaluated for arbitrary preferences. In this note, we offer a solution to the issue, which relies on a slight modification of the stock’s payoff structure and supports all the conclusions of the paper. 1 The problem The expression for the conditional expected utility Ej(U(W2j) | Fj) stated on page 906 is correct. However, equation 12 obtained by taking its unconditional expectation is not. To see why, we rewrite Ej(U(W2j) | Fj) as: Ej(U(W2j) | Fj) = U(W0j) + U (W0j)Ej(∆W | Fj) + 1 2 U (W0j)Ej(∆W 2 | Fj) + o(z), (1)

Capital Gains: A Critique

The following discussion brings to the forefront the present treatment of capital gains. It joins the line of commentary that is generally critical of the present capital gain provisions on the basis of inadequate justification for the substantial and what is argued to be arbitrary preference, which in itself is based on a historical tradition and theoretical argument that hardly holds water in the modern age. At the same time, this piece stops short of advocating a radical reform of the capital gains treatment. Before any drastic action in this arena can be undertaken, a much more complete and thorough study of the myriad of interconnected issues is in line.

Contract as Equitable Instrument - Sensibility in Indian Contract Act

Equity, which means equalization or levelling down any arbitrary preferences or denial of justice, is derived from a Roman term ‘aequitas’. According to Sir Henry Mane, equity is fresh body of rules by the side of the original founded on distinct principles and claiming to supersede the law by virtue of a superior sanctity inherent in those principles. Inadequacy of the remedies at law and the elastic willingness of equity to use its discretion directly with reference to the conscience of the individual were two main foundations of equitable belief. Equity is aimed at preventing a defendant from acting unconscionably (literally, contrary to conscience) in circumstances otherwise where the common law would have allowed to do so. In layman’s language it can be said to interfering to protect some underlying right of the victim either because of a contract with the shyster, or because the shyster has control over some property which is rightfully theirs or because one may feel that the actions of the shyster may affect the victim in the future in some way or the other. Most of the equitable principles and rules have, in India, been embodied in the statute law and has been made applicable to the extent of the provisions made therein. That, the provisions of equity in Indian statute books might have their source in common law or in equity or in an adjustment between the two, is immaterial.The equitable doctrines featuring in the Indian Contract Act are mainly, the doctrine of penalties and forfeiture, stipulations as to time in a contract, equitable relief on the ground of misrepresentation, fraud and undue influence.The statutory recognition of the principles of equity in the Specific Relief Act is regarding injunction, specific performance, cancellation, rectification and recession etc. Incorporation of the maxim in Indian Laws Aequitas sequitur legem i.e. equity follows the law – Equity does not claim to override the law. Equity generally operates by recognising the legal rule and adding some further rule, remedy or the other machinery of its own. The Court of Chancery, which developed equitable law never wanted to give the equity an overriding effect to the common law. The jurisdiction of equity is debarred from overreaching the boundaries established by the prior course of adjudication.Another maxim which needs a mention in this discussion is 'Aeguitas nunquam contravenit leges' i.e., equity never counteracts law. In India, since there is no distinction between a legal interest and equitable interest, therefore, in all matters relating to legal as well as equitable interests, the statutory provisions shall apply if there are any.Section 38 of the Specific Relief Act provides that on adjudging recession of a contract, the Court may require the party to whom such relief in granted, to make any compensation to the other which justice may require. Section 30 and 38 also provide that on adjudging the cancellation of an instrument, the Court may require the party to whom such relief is granted, to make compensation to the other which justice may require.Though equity was faced with conflict with the laws in England in the earlier stages, it has always played a major role in the Law of Contracts. The Indian Contract Act lays that consent to an agreement is caused by undue influence, the argument is a contract voidable at the option of the party whose consent was so caused. Any such contract may be set aside either absolutely or, if the party who was entitled to avoid it, has received any benefit there under, upon such terms and conditions as the court may deem first. (Section 19A) Further section 64 and 65 of the Indian Contract Act are also based on the doctrine ‘he who seeks equity must do equity’. The maxim, however, does not apply when relief sought by the plaintiff and equitable right or relief secured to or sought by the defendant belongs to or originates from two entirely separate and distinct matters. Further, it is not applicable where the plaintiff seeks to enforce purely legal rights. Other provisions giving effect to the maxim Equity delights in equality are section 42 of the Indian Contract Act that applies the principle of tenancy-in-common, section 43, 63-70,146-147 of the Indian Contract Act.

When Is Shuttle Diplomacy Worth the Commute? Information Sharing through Mediation

The authors study the conflict mediation problem, sometimes called “shuttle diplomacy,” when the mediator acts as a go-between and must gather information from the disputants. In the context of a general model of information mediation, they show that the incentive that disputants have to lie to the mediator undoes any advantage that might be gained by adding communication with a third party. In fact, the main result shows that any equilibrium outcome that is achievable through mediation is also achievable as an equilibrium outcome of a game with unmediated preplay communication. This is true even when the mediator is allowed to have arbitrary preferences or biases. The authors then test their empirical prediction on dispute management efforts between 1937 and 1985. The analysis supports the hypothesis that information mediation has no effect in environments where the mediator has no independent source of information.

Optimal Securitization with Heterogeneous Investors

We solve the problem of optimal securitization for an issuer facing heterogeneous investors with arbitrary time and risk preferences. We show that the optimal securitization is characterized by multiple nonlinear tranches, and each investor gets a portfolio of these tranches. In particular, when all agents have CARA utilities, the linear tranching is optimal, with the number of tranches being less than or equal to the number of investors. To the best of our knowledge, this is the first model in the literature that explains the appearance of multiple tranches in the security design and the relation of the tranche thresholds to microeconomic characteristics. We show that the boundaries of the tranches can be efficiently calculated through a fixed point of a contraction mapping, and we develop new powerful techniques that are generally applicable for numerical calculation of constrained Pareto-efficient allocations. We use these contraction mapping techniques to derive a number of comparative static results for optimal securitization. The model generates theoretical predictions and numerical simulations that agree with several recent empirical findings concerning the CDO structure.

Co-monotonicity of optimal investments and the design of structured financial products

We prove that, under very weak conditions, optimal financial products on complete markets are co-monotone with the reversed state price density. Optimality is meant in the sense of the maximization of an arbitrary preference model, e.g., expected utility theory or prospect theory. The proof is based on a result from transport theory. We apply the general result to specific situations, in particular the case of a market described by the Capital Asset Pricing Model or the Black–Scholes model, where we derive a generalization of the two-fund-separation theorem and give an extension to APT factor models and structured products with several underlyings. We use our results to derive a new approach to optimization in wealth management, based on a direct optimization of the return distribution of the portfolio. In particular, we show that optimal products can (essentially) be written as monotonic functions of the market return. We provide existence and nonexistence results for optimal products in this framework. Finally we apply our results to the study of bonus certificates, show that they are not optimal, and construct a cheaper product yielding the same return distribution.

A Bird in the Microcosm: An Environment of Found Objects Constructed to Create Arbitrary Preferences in Starlings

The human environment consists of objects and temporal relations arranged so as to manipulate our attention, learning, preferences and behavior. Our physical environments and organizational institutions create constraints on and guarantees of the future behaviors of ourselves and others [1,2]. It is crucial not just to document or subvert these institutions but also to create the ones that we imagine and need. Here I describe my approach to this challenge. Constraints on behavior are an outcome of social and embodied manipulation of our attention and learning. The mating display of a male bird has evolved to attract the attention of the female, elicit her approach and, through a series of coordinated ritualized actions, to bring both to simultaneous states of arousal [3,4]. In an ad hoc manner, we create similar relations of anticipation and coordination between ourselves and other people and things [5]. Consistent behavioral feedback helps others to anticipate our reactions and can lead to happier coexistence [6]. To achieve the self-control required for consistency, we rely on environments and organizational institutions to guarantee and constrain our interactions. Physical objects, both natural and cultural, communicate their function to us by taking advantage of our psychology—for example, our attentional biases and learning [7]. Rather than reacting haphazardly to the industrial products and ephemeral activities of others, I practice the construction of environments. Although some conceptual or “open systems” art appears solipsistic [8], it also provides a precedent. Beuys’s 1974 work I Like America and America Likes Me, for example, involved symbolic yet ambiguous interstarlings; that is, a behavioral constraint was brought about by inducing the observer starling to focus attention on the tutor (see Fig. 1). The design of the arena and equipment was critical to guaranteeing the starlings’ preferences and behaviors. Light from lamps enticed the starlings in and out of the arena and focused their attention. A sloping roof inhibited fl ight, allowing feeding behavior. As the operator, I too effectively became a part of the “machine.” The apparatus acted as a prosthesis [13], but it was not simply an extension of my capacities. It was also a constraint on possible/permissible behaviors. If I became impatient, the starlings became nervous. When moving parts stuck, if I forgot what to do, or if a starling escaped, the motivational and behavioral balance of our interaction faltered. This interactive construction was both a microcosm and a metaphor for other institutions. While I can get “results” from my interactions with starlings, a rich and provocative aspect of this humanmachine-animal system is how the process of the artwork helps us to rethink nature and our transformations of it. actions between Beuys and a coyote living together in a gallery in New York [9,10]. Today, the alteration of natural habitats and urbanization of species causes confl ict [11], while geographers have called for a “re-animation” of our conceptualization of human environments [12]. In response to these ideas, I designed an environment to constrain the attention, actions and preferences not only of myself but of another species as well. Using found objects, including a cage, anglepoise lamps, a puppet theater, a collapsed chair on wheels, a garbage bag and picnic-ware, I constructed an arena for starlings (held under a license from English Nature). Starlings are gregarious birds inhabiting farms and cities and thus already participating in our modifi ed environments. In this arena, an observer starling watched a trained tutor starling eat mealworms from one of two bowls or eggcups. After the tutor left the arena, the observer starling entered and could choose between the two bowls of mealworms. Fourteen starlings experienced one such session each, and a preference for eating from the demonstrated bowl was seen in the majority of observer AR TS C IE N C E: T H E ES S EN TI AL C O N N EC TI O N

A General Framework for Expressing Preferences in Causal Reasoning and Planning

We consider the problem of representing arbitrary preferences in causal reasoning and planning systems. In planning, a preference may be seen as a goal or constraint that is desirable, but not necessary, to satisfy. To begin, we define a very general query language for histories, or interleaved sequences of world states and actions. Based on this, we specify a second language in which preferences are defined. A single preference defines a binary relation on histories, indicating that one history is preferred to the other. From this, one can define global preference orderings on the set of histories, the maximal elements of which are the preferred histories. The approach is very general and flexible; thus it constitutes a ‘base’ language in terms of which higher-level preferences may be defined. To this end, we investigate two fundamental types of preferences that we call choice and temporal preferences. We consider concrete strategies for these types of preferences and encode them in terms of our framework. We suggest how to express aggregates in the approach, allowing, e.g. the expression of a preference for histories with lowest total action costs. Last, our approach can be used to express other approaches and so serves as a common framework in which such approaches can be expressed and compared. We illustrate this by indicating how an approach due to Son and Pontelli can be encoded in our approach, as well as the language PDDL3.

Interspecific Social Learning: Novel Preference Can Be Acquired from a Competing Species

Nongenetic transmission of behavioral traits via social learning allows local traditions in humans, and, controversially, in other animals [1-4]. Social learning is usually studied as an intraspecific phenomenon (but see [5-7]). However, other species with some overlap in ecology can be more than merely potential competitors: prior settlement and longer residence can render them preferable sources of information [8]. Socially induced acquisition of choices or preferences capitalizes upon the knowledge of presumably better-informed individuals [9] and should be adaptive under many natural circumstances [10, 11]. Here we show with a field experiment that females of two migrant flycatcher species can acquire a novel, arbitrary preference of competing resident tits for a symbol attached to the nest sites. The experiment demonstrates that such blind acquisition of heterospecific traits can occur in the wild. Even though genetic variation for habitat preferences exists in many taxa [12] and overlap between bird species likely induces costs [13], this result shows that interspecific social learning can cause increased overlap in nest-site preferences. Conventional, negative species interactions push ecological niches of species apart, but the use of competing species as a source of information counters that force and may lead to convergence.

Co-Monotonicity of Optimal Investments and the Design of Structured Financial Products

We prove that under very weak conditions optimal financial products have to be co-monotone with the inverted state price density. Optimality is meant in the sense of the maximization of an arbitrary preference model, e.g. Expected Utility Theory or Prospect Theory. The proof is based on methods from transport theory. We apply the general result to specific situations, in particular the case of a market described by the Capital Asset Pricing Model, where we derive an extension of the Two-Fund-Separation Theorem. We use our results to derive a new approach to optimization in wealth management, based on a direct optimization of the return distribution of the portfolio.We provide existence and non-existence results for optimal products in this framework. Finally we apply our results to the study of down-and-out barrier options, show that they are not optimal and describe a construction of a cheaper product yielding the same return distribution.

Information and the Equity Premium

We consider the effect of information on the ex ante average risk-free rate and the equity premium in a standard exchange economy with a representative agent. We show that information always increases the average risk-free rate. Clearly, perfect information eliminates the equity premium; moreover, we show that a particular kind of information about the level of the return to equity always decreases the average equity premium. Surprisingly, however, information must sometimes raise the ex ante premium, no matter what the preferences of the representative agent; and information purey about the volatility of the return always raises the equity premium for a interesting class of preferences. We consider two different economies: a two-period model with arbitrary preferences for the representative agent; and an infinite horizon model with additive separable CES utility with independent growth rates.

Principles of Equity and Contracts

English law before the introduction of the principle of equity was mainly governed by Common Law (Commune Ley). Blackstone defined Common Law as the municipal law of England or the rule of civil conduct prescribed to the inhabitants of the kingdom. But this system of common law had certain flaws as it did not provide for any remedy in many cases where one was required. This thus paved the requirement for the emergence of the principles of equity and the decisions were given in good conscience. Equity which means equalization or leveling down any arbitrary preferences or denial of justice is derived from a Roman term 'aequitas'. According to Sir Henry Mane, equity is fresh body of rules by the side of the original founded on distinct principles and claiming to supercede the law by virtue of a superior sanctity inherent in those principles. Equity is aimed at preventing a defendant from acting unconscionably (literally, contrary to conscience) in circumstances otherwise where the common law would have allowed to do so. In layman's language it can be said to interfering to protect some underlying right of the victim either because of a contract with the shyster, or because the shyster has control over some property which is rightfully theirs or because one may feel that the actions of the shyster may affect the victim in the future in some way or the other. Though equity was faced with conflict with the laws in England in the earlier stages, it always had always played a major role in the Law of Contracts. Equity in contracts can be seen in the fields of restitution, unjust enrichment, mistake and estoppel. In the subsequent chapters the researcher intends to analyze the role of the Principle of Equity in Contracts. The researcher would like to look into the nature of equity to bring about a relationship between equity and contracts. One must also understand the doctrine of Specific Performance would also be looked into as it is major area in the case of Contracts where equity plays a significant role. The researcher would look into the Contracts where Specific Performance is available and those where it is not available. Though this project aims to cover most of the field areas under the abovementioned topic it has certain limitations. The researcher during his research would not concentrate on the history of equity and its origin. It would concentrate majorly on mistake, unjust enrichment and Specific Performance. He would not go into a great depth and analyze the equity in the Indian Contract Act. Neither would he look into the issue of Quasi-Contracts which include the principles of equity in it. As this is mostly a critical analysis the researcher would not like to venture much into the Indian cases rather he would look mostly into the English Law to analyze this relationship. The researcher would also like to point out the fact that the topics that he would be covering are in themselves a separate area where extensive research has been done on. Given the time and space restraint the researcher would be unable to cover all these areas to the extent they have been discussed in by various jurists. The researcher would give a sincere effort in order to explain to its readers the importance of the Principle of equity in Contract Law and apologizes for any unintended error that may be caused the course of this project. HYPOTHESIS The researcher intends to provide the readers with a critical analysis of the Principles of Equity and their application in the Law of Contracts. The researcher does feel that the Contract law which have certain loopholes and their advantage are taken by a certain party whereas the other suffers. The researcher thus hypothesizes that the Contract Law would have been insufficient if these principles were not applied.

Options can induce risk taking for arbitrary preferences

It is widely believed that call options induce risk-taking behavior. However, Ross (2004) challenges this intuition by demonstrating the impossibility of inducing managers with arbitrary preferences to always act as if they were less risk averse. If preferences and price distributions are unknown, risk-taking behavior cannot be always induced by an option contract. Here, we prove a new result showing that, with no information about preferences and some knowledge about prices, one can write a call option that makes all managers prefer riskier projects to safer ones. This points out that in order to design options that induce risk taking it is sufficient to have information about price distributions.

Options Can Induce Risk Taking for Arbitrary Preferences

It is widely believed that call options induce risk-taking behavior. However, Ross (2003) challenges this intuition by demonstrating the impossibility of inducing managers with arbitrary preferences to always act as if less risk averse. If preferences and price distributions are unknown, risk-taking behavior cannot be induced by options. Here, we prove a new result showing that, with absolutely no information about preferences and some knowledge about prices, one can write a call option that makes all managers prefer riskier projects to safer ones. This points out that in order to design options that induce risk taking it is sufficient to have information about price distributions.

Strategy/False-name Proof Protocols for Combinatorial Multi-Attribute Procurement Auction

In this paper, we investigate a model of a combinatorial, procurement multi-attribute auction, in which each sales item is defined by several attributes called quality, the buyer is the auctioneer (e.g., a government), and the sellers are the bidders. Furthermore, there exist multiple items and both buyer and sellers can have arbitrary (e.g., substitutable/complementary) preferences on a bundle of items. Our goal is to develop a protocol that is strategy-proof for sellers. We first present a VCG-type protocol. As in a standard combinatorial auction, a VCG-type protocol is not false-name-proof, i.e., it is vulnerable against manipulations using multiple identifiers. Next, we show that any strategy-proof protocol in this model can be represented as a framework called Price-Oriented Rationing-Free (PORF) protocol, in which for each bidder, for each bundle of items, and for each quality, the payment for the bidder is determined independently of his own declaration, and the bidder can obtain a bundle that maximizes his utility independently of the allocations of other bidders. We develop a false-name-proof protocol in this model.

Ordered Mean Difference Benchmarking, Utility Generators, and Capital Market Equilibrium

Designed as a fund performance measure, the ordered mean difference is extended to characterize zero‐surplus situations, such as a capital market equilibrium generated by arbitrary risk preferences. This enables nonparametric testing for whether CAPM applies and the detection of pricing inefficiencies or anomalies from historical data, including international capital market segmentation. Any risk‐averse utility function can be decomposed into a weighted average of elementary put option profiles (“gnomic” utility functions), which collectively generate the OMD areas. The investor's risk profile can be summarized as a representative gnome, so can the market risk premium. Pricing efficiency turns on whether such a representative gnome exists.