Online Learning with Switching Costs and Other Adaptive Adversaries

We study the power of different types of adaptive (nonoblivious) adversaries in the setting of prediction with expert advice, under both full-information and bandit feedback. We measure the player's performance using a new notion of regret, also known as policy regret, which better captures the adversary's adaptiveness to the player's behavior. In a setting where losses are allowed to drift, we characterize ---in a nearly complete manner--- the power of adaptive adversaries with bounded memories and switching costs. In particular, we show that with switching costs, the attainable rate with bandit feedback is $\widetilde{\Theta}(T^{2/3})$. Interestingly, this rate is significantly worse than the $\Theta(\sqrt{T})$ rate attainable with switching costs in the full-information case. Via a novel reduction from experts to bandits, we also show that a bounded memory adversary can force $\widetilde{\Theta}(T^{2/3})$ regret even in the full information case, proving that switching costs are easier to control than bounded memory adversaries. Our lower bounds rely on a new stochastic adversary strategy that generates loss processes with strong dependencies

Arbitrage and viability in securities markets with fixed trading costs

This paper studies foundational issues in securities markets models with fixed costs of trading, i.e. transactions costs that are bounded regardless of the transaction size, such as fixed brokerage fees, investment taxes, operational, and processing costs or opportunity costs. We show that the absence of free lunches in such models is equivalent to the existence of a family of absolutely continuous probability measures for which the normalized securities price processes are martingales. This is a weaker condition than the absence of free lunch in frictionless models, which is equivalent to the existence of an equivalent martingale measure. We also show that the only arbitrage-free pricing rules on the set of attainable contingent claims are those that are equal to the sum of an expected value with respect to any absolutely continuous martingale measure and of a bounded fixed cost functional. Moreover, these pricing rules are the only ones to be viable as models of economic equilibrium.Arbitrage, Fixed costs, Absolutely continuous Martingale measure, Contingent claims pricing

Good deals in markets with frictions

This paper studies a portfolio choice problem such that the pricing rule may incorporate transaction costs and the risk measure is coherent and expectation bounded. We will prove the necessity of dealing with pricing rules such that there are essentially bounded stochastic discount factors, which must be also bounded from below by a strictly positive value. Otherwise good deals will be available to traders, i.e., depending on the selected risk measure, investors can build portfolios whose (risk, return) will be as close as desired to (- infinite, + infinite) or (0, infinite). This pathologic property still holds for vector risk measures (i.e., if we minimize a vector valued function whose components are risk measures). It is worthwhile to point out that essentially bounded stochastic discount factors are not usual in financial literature. In particular, the most famous frictionless, complete and arbitrage free pricing models imply the existence of good deals for every coherent and expectation bounded measure of risk, and the incorporation of transaction costs will no guarantee the solution of this caveatRisk measure, Perfect and imperfect markets, Stochastic discount factor, Portfolio choice model, Good deal

Shadow prices for continuous processes

In a financial market with a continuous price process and proportional transaction costs we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process, i.e.~a least favorable frictionless market leading to the same optimal strategy and utility as in the original market under transaction costs. The crucial ingredients are the continuity of the price process and the hypothesis of "no unbounded profit with bounded risk". A counter-example reveals that these hypotheses cannot be relaxed

On the Economic Order Quantity Model With Transportation Costs

We consider an economic order quantity type model with unit out-of-pocket holding costs, unitopportunity costs of holding, fixed ordering costs and general transportation costs. For these models, we analyzethe associated optimization problem and derive an easy procedure for determining a bounded interval containingthe optimal cycle length. Also for a special class of transportation functions, like the carload discount schedule, wespecialize these results and give fast and easy algorithms to calculate the optimal lot size and the correspondingoptimal order-up-to-level.EOQ-type model;exact solution;transportation cost function;upper bounds

The Problem With Bounded Rationality On Behavioral Assumptions in the Theory of the Firm

I discuss and compare alternative approaches to integrating bounded rationality with the theory of economic organization, concentrating on the organizational capabilities approach, which is strongly influenced by the works of Nelson and Winter, organizational economics, particularly transaction cost economics, and, finally, a small subset of the literature on biases to judgment and cognition. I argue that, contrary to the conventional view, both the organizational capabilities approach and transaction cost economics treat bounded rationality rather “thinly,” the former being in actuality more taken up with organizational routines than individual boundedly rational behavior, the latter only invoking bounded rationality to the extent that it helps explaining incompleteness of contracting. The rich literature on cognitive biases, etc. suggests a “thick” approach to bounded rationality that may be helpful with respect to furthering the theory of economic organization. Examples pertaining to the internal organization of firms are provided.capability, organizations, transaction costs

Specialization, Information, and Growth: A Sequential Equilibrium Analysis

Pricing costs and information problems are introduced into a framework with consumer-producers, economies of specialization, and transaction costs to predict the endogenous and concurrent evolution in division of labor and in the information of organization acquired by society. The concurrent evolution generates endogenous growth based on the tradeoff between gains from information about the efficient pattern of division of labor, which can be acquired via experiments with various patterns of division of labor, and experimentation costs, which relate to the costs in discovering prices. The concept of Walras sequential equilibrium is developed to analyze the social learning process which is featured with uncertainties of the direction of the evolution as well as a certain trend of the evolution.Coevolution of specialization and information, adaptive decision, bounded rationality, sequential equilibrium, economic development.