Breaking the Cycle: How the News and Markets Created a Negative Feedback Loop in COVID-19
New research from CBS Professor Harry Mamaysky reveals how negativity in the news and markets can escalate a financial crisis.
New research from CBS Professor Harry Mamaysky reveals how negativity in the news and markets can escalate a financial crisis.
Adapted from “Global Value Chains in Developing Countries: A Relational Perspective from Coffee and Garments,” by Laura Boudreau of Columbia Business School, Julia Cajal Grossi of the Geneva Graduate Institute, and Rocco Macchiavello of the London School of Economics.
Adapted from “Online Advertising as Passive Search,” by Raluca M. Ursu of New York University Stern School of Business, Andrey Simonov of Columbia Business School, and Eunkyung An of New York University Stern School of Business.
This paper from Columbia Business School, “Meaning of Manual Labor Impedes Consumer Adoption of Autonomous Products,” explores marketing solutions to some consumers’ resistance towards autonomous products. The study was co-authored by Emanuel de Bellis of the University of St. Gallen, Gita Johar of Columbia Business School, and Nicola Poletti of Cada.
Co-authored by John B. Donaldson of Columbia Business School, “The Macroeconomics of Stakeholder Equilibria,” proposes a model for a purely private, mutually beneficial financial agreement between worker and firm that keeps decision-making in the hands of stockholders while improving the employment contract for employees.
At Columbia Business School, our faculty members are at the forefront of research in their respective fields, offering innovative ideas that directly impact the practice of business today. A quick glance at our publication on faculty research, CBS Insights, will give you a sense of the breadth and immediacy of the insight our professors provide.
As a student at the School, this will greatly enrich your education. In Columbia classrooms, you are at the cutting-edge of industry, studying the practices that others will later adopt and teach. As any business leader will tell you, in a competitive environment, being first puts you at a distinct advantage over your peers. Learn economic development from Ray Fisman, the Lambert Family Professor of Social Enterprise and a rising star in the field, or real estate from Chris Mayer, the Paul Milstein Professor of Real Estate, a renowned expert and frequent commentator on complex housing issues. This way, when you complete your degree, you'll be set up to succeed.
Columbia Business School in conjunction with the Office of the Dean provides its faculty, PhD students, and other research staff with resources and cutting edge tools and technology to help push the boundaries of business research.
Specifically, our goal is to seamlessly help faculty set up and execute their research programs. This includes, but is not limited to:
All these activities help to facilitate and streamline faculty research, and that of the doctoral students working with them.
This survey reviews the forty-year history of research on transportation revenue management (also known as yield management). We cover developments in forecasting, overbooking, seat inventory control, and pricing, as they relate to revenue management, and suggest future research directions. The survey includes a glossary of revenue management terminology and a bibliography of over 190 references.
This paper develops a variance reduction technique for Monte Carlo simulations of path-dependent options driven by high-dimensional Gaussian vectors. The method combines importance sampling based on a change of drift with stratified sampling along a small number of key dimensions. The change of drift is selected through a large deviations analysis and is shown to be optimal in an asymptotic sense. The drift selected has an interpretation as the path of the underlying state variables which maximizes the product of probability and payoff—the most important path.
This paper addresses the simultaneous determination of pricing and inventory replenishment strategies in the face of demand uncertainty. More specifically, we analyze the following single item, periodic review model. Demands in consecutive periods are independent, but their distributions depend on the item's price in accordance with general stochastic demand functions. The price charged in any given period can be specified dynamically as a function of the state of the system. A replenishment order may be placed at the beginning of some or all of the periods. Stockouts are fully backlogged.
This paper develops methods for relating the prices of discrete- and continuous-time versions of path-dependent options sensitive to extremal values of the underlying asset, including lookback, barrier, and hindsight options. The relationships take the form of correction terms that can be interpreted as shifting a barrier, a strike, or an extremal price. These correction terms enable us to use closed-form solutions for continuous option prices to approximate their discrete counterparts.
This paper develops methods for relating the prices of discrete- and continuous-time versions of path-dependent options sensitive to extremal values of the underlying asset, including lookback, barrier, and hindsight options. The relationships take the form of correction terms that can be interpreted as shifting a barrier, a strike, or an extremal price. These correction terms enable us to use closed-form solutions for continuous option prices to approximate their discrete counterparts.
This paper describes a family of discrete-review policies for scheduling open multiclass queueing networks. Each of the policies in the family is derived from what we call a dynamic reward function: such a function associates with each queue length vector q and each job class k a positive value rk(q), which is treated as a reward rate for time devoted to processing class k jobs. Assuming that each station has a traffic intensity parameter less than one, all policies in the family considered are shown to be stable.
We analyze a general model of dynamic vehicle dispatching systems in which congestion is the primary measure of performance. In the model, a finite collection of tours are dynamically dispatched to deliver loads that arrive randomly over time. A load waits in queue until it is assigned to a tour. This representation, which is analogous to classical set-covering models, can be used to study a variety of dynamic routing and load consolidation problems.
This paper develops methods for fast estimation of option price sensitivities in Monte Carlo simulation of term structure models. The models considered are based on discretely compounded forward rates with proportional volatilities. The efficient estimation of option deltas, gammas, and vegas are investigated in this setting.
The bottleneck in a production-inventory network is commonly taken to be the facility that most limits flow through the network and thus the most highly utilized facility. A further connotation of "bottleneck," however, is the facility that most constrains system-wide performance or the facility at which additional resources would have the greatest impact.
We analyze the performance of a splitting technique for the estimation of rare event probabilities by simulation. A straightforward estimator of the probability of an event evaluates the proportion of simulated paths on which the event occurs. If the event is rare, even a large number of paths may produce little information about its probability using this approach. The method we study reinforces promising paths at intermediate thresholds by splitting them into subpaths which then evolve independently.
Consider a category of product variants distinguished by some attribute such as color or flavor. A retailer must construct an assortment for the category, i.e., select a subset variants to stock and determine purchase quantities for each offered variant. We analyze this problem using a multinomial logit model to describe the consumer choice process and a newsboy model to represent the retailer's inventory cost. We show that the optimal assortment has a simple structure and provide insights on how various factors affect the optimal level of assortment variety.
Contemporary management theories such as Just-in-Time and Total Quality Management emphasize variance reduction as a critical step in improving system performance. But little is said about how such efforts should be directed. Suppose a manager has only limited resources for variance reduction efforts. How should she allocate them among a set of competing activities? Which activity should receive highest priority?
We describe effective time partitioning heuristics for dynamic lot-sizing problems in multiitem and multilocation production/distribution systems. In a time-partitioning heuristic, the complete horizon of (say) N periods, is partitioned into smaller intervals. An instance of the problem is solved, to optimality, on each of these intervals, and the resulting solution coalesced into a solution for the complete horizon. The intervals are selected to be of a size which permits the use of exact and effective solution methods (e.g., branch-and-bound methods).
This paper concerns the modeling of low inventory lines. Currently, most models assume that processing times are independent. We consider the differences in behavior of workers in low- and high-inventory production lines. Using a laboratory experiment we show that workers speed up whent hey are the cause of idle time on the line. This means that processing time distributions are not independent of the size of the buffer, of the processing speed of co-workers, or of the amount of inventory in the system.
In this paper we develop policies for scheduling dynamically arriving jobs to a broad class of parallel-processing queueing systems. We show that in heavy traffic the policies asymptotically minimize a measure of the expected system backlog, which we call system work. Our results yield succinct, closed-form expressions for optimal system work in heavy traffic.
We study the Mt/G/∞ queue where customers arrive according to a sinusoidal function λt = λ + A sin(2 π t/T) and the service rate is μ. We show that the expected number of customers in the system during peak congestion can be closely approximated by (λ + A)/ μ for service distributions with coefficient of variation between 0 and 1.
We study the Mt/G/∞ queue where customers arrive according to a sinusoidal function λt = λ + A sin(2 π t/T) and the service rate is μ. We show that the expected number of customers in the system during peak congestion can be closely approximated by (λ + A)/ μ for service distributions with coefficient of variation between 0 and 1.
We show how a simple normal approximation to Erlang's delay formula can be used to analyze capacity and staffing problems in service systems that can be modeled as M/M/s queues.
We show how a simple normal approximation to Erlang's delay formula can be used to analyze capacity and staffing problems in service systems that can be modeled as M/M/s queues.
The increased complexity of modern manufacturing has led to uncertainties in production processes. Factors such as unplanned machine maintenance, tool unavailability, and complex process adjustments make it difficult to maintain a predictable level of output. To be effective, an appropriate production model must incorporate these uncertainties into the representation of the production process. This paper considers a one-time production of an application-specific product which must follow a fixed routing through the manufacturing system.
Why has the service factory model failed to live up to its original promise? To answer this question, we start with a basic concept: service is doing the work of your customer. As a result, it requires a high level of contact, communication and coordination with your customers. To deliver truly excellent service, therefore, requires a level of customer intimacy. That is, a service provider needs to know individual customers being served in order to deliver service that, in addition to being efficient, is also personal and effective in fulfilling their total service requirements.
Why has the service factory model failed to live up to its original promise? To answer this question, we start with a basic concept: service is doing the work of your customer. As a result, it requires a high level of contact, communication and coordination with your customers. To deliver truly excellent service, therefore, requires a level of customer intimacy. That is, a service provider needs to know individual customers being served in order to deliver service that, in addition to being efficient, is also personal and effective in fulfilling their total service requirements.
We examine some mathematical aspects of learning unknown mappings with the mixture of experts model (MEM). Specifically, we observe that the MEM is at least as powerful as a class of neural networks, in a sense that will be made precise. Upper bounds on the approximation error are established for a wide class of target functions. The general theorem states that ||f-fn||p⩽c/nr d/ for f∈Wpr(L) (a Sobolev class over [-1,1]d), and fn belongs to an n-dimensional manifold of normalized ridge functions.
To improve the efficiency of product distribution for a centralized bakery, I first performed each person's tasks and discovered that constructing optimal minimum-distance routes would not significantly reduce costs but replacing the physical validation of new routes with a manual mathematical computation or simulation would. The trick was getting management to trust the simulation enough to use it.
This note gives a simple proof that in a (r, q) system the average outstanding backorders andthe average stockouts per unit time are jointly convex in the two control variables q and r.
This note gives a simple proof that in a (r, q) system the average outstanding backorders andthe average stockouts per unit time are jointly convex in the two control variables q and r.
A major problem in forecasting is estimating the time of some future event. Traditionally, forecasts are designed to minimize an error cost function that is evaluated once, possibly when the event occurs and forecast accuracy can be determined. However, in many applications forecast error costs accumulate over time, and the forecasts themselves may be updated with information that is collected as the expected time of the event approaches. This paper examines one such application, in which flow control managers in the U.S.
Bid-prices are becoming an increasingly popular method for controlling the sale of inventory in revenue management applications. In this form of control, threshold—or "bid"—prices are set for the resources or units of inventory (seats on flight legs, hotel rooms on specific dates, etc.) and a product (a seat in a fare class on an itinerary or room for a sequence of dates) is sold only if the offered fare exceeds the sum of the threshold prices of all the resources needed to supply the product.
The accelerated pace of technological change has led to rapid obsolescence of productive capacity in electronics and other industries. Managers must consider the impact of future technologies while making acquisition and replacement decisions in such environments. We consider a problem where a sequence of technological breakthroughs are anticipated but their magnitude and timing are uncertain. A firm, operating in such an environment, must decide how much capacity of the current technology to acquire to meet future demand growth.
In this paper we address periodic base-stock policies for stochastic economic lot scheduling problems. These represent manufacturing settings in which multiple items compete for the availability of a common capacity source, in the presence of setup times and/or costs, incurred when switching between items, and in the presence of uncertainty regarding demand patterns, production, and setup times. Under periodic base-stock policies, items are produced according to a given periodic item-sequence.
This paper studies the trade-off between inventory levels and the delivery leadtime offered to customers in achieving a target level of service. It addresses the question of how much a delivery leadtime can be reduced, per unit increase of inventory, at a fixed fill rate. We show that for a class of assemble-to-order models with stochastic demands and production intervals there is a simple linear trade-off between inventory and delivery leadtime, in a limiting sense, at high fill rates.
We determine the minimum cost of super-replicating a nonnegative contingent claim when there are convex constraints on portfolio weights. We show that the optimal cost with constraints is equal to the price of a related claim without constraints. The related claim is a dominating claim, that is, a claim whose payoffs are increased in an appropriate way relative to the original claim. The results hold for a variety of options, including some path-dependent options.
We consider a distribution system consisting of a single warehouse and many geographically dispersed retailers. Each retailer faces demands for a single item which arise a deterministic, retailer specific rate. The retailers' stock is replenished by a fleet of vehicles of limited capacity, departing and returning to the warehouse and combining deliveries into efficient routes. The cost of any given route consists of a fixed component and a component which is proportional with the total distance driven. Inventory costs are proportional with the stock levels.
A guiding principle in the efficient estimation of rare-event probabilities by Monte Carlo is that importance sampling based on the change of measure suggested by a large deviations analysis can reduce variance by many orders of magnitude. In a variety of settings, this approach has led to estimators that are optimal in an asymptotic sense. We give examples, however, in which importance sampling estimators based on a large deviations change of measure have provably poor performance.
Global brands represent enormous cash-producing assets. To build them requires consistency over time and across country borders. The key for developing consistent strategy across country borders is identifying the global segment and the global position. The key for implementing that strategy is often the global marketing team.
We analyze a multistage inventory system with limited production capacity facing stochastic demands. Each node follows a periodic-review base-stock policy for echelon inventory: in each period, each node attempts to produce enough material to restore cumulative down-stream inventory to a fixed target level. We develop approximations to the key measures of interest (average inventories, average backorders, and service levels) by simultaneously letting the mean demand approach the system's bottleneck capacity and letting the base-stock level for finished goods increase without bound.
The payoff of a barrier option depends on whether or not a specified asset price, index, or rate reaches a specified level during the life of the option. Most models for pricing barrier options assume continuous monitoring of the barrier; under this assumption, the option can often be priced in closed form. Many (if not most) real contracts with barrier provisions specify discrete monitoring instants; there are essentially no formulas for pricing these options, and even numerical pricing is difficult.
The payoff of a barrier option depends on whether or not a specified asset price, index, or rate reaches a specified level during the life of the option. Most models for pricing barrier options assume continuous monitoring of the barrier; under this assumption, the option can often be priced in closed form. Many (if not most) real contracts with barrier provisions specify discrete monitoring instants; there are essentially no formulas for pricing these options, and even numerical pricing is difficult.
A firm has inventories of a set of components that are used to produce a set of products. There is a finite horizon over which the firm can sell its products. Demand for each product is a stochastic point process with an intensity that is a function of the vector of prices for the products and the time at which these prices are offered. The problem is to price the finished products so as to maximize total expected revenue over the finite sales horizon. An upper bound on the optimal expected revenue is established by analyzing a deterministic version of the problem.
We develop bounds and approximations for setting base-stock levels in production-inventory systems with limited production capacity. Our approximations become exact as inventories become critical, meaning either that the target service level is very high or the backorder penalty is very large. Our bounds apply even without this requirement. We consider both single-stage and multi-stage systems.
We consider the problem of estimating a density function from a sequence of independent and identically distributed observations xi taking value in Rd. The estimation procedure constructs a convex mixture of "basis" densities and estimates the parameters using the maximum likelihood method.
A methodology to price American options with finitely many exercise opportunities simulates the evolution of underlying assets via random trees that branch at each of the possible early exercise dates. From these trees, two consistent price estimates are obtained, one biased high and one biased low. These two estimates can be combined to provide a valid, though conservative confidence interval for the option price.
A methodology to price American options with finitely many exercise opportunities simulates the evolution of underlying assets via random trees that branch at each of the possible early exercise dates. From these trees, two consistent price estimates are obtained, one biased high and one biased low. These two estimates can be combined to provide a valid, though conservative confidence interval for the option price.
We consider the problem of scheduling N jobs on M parallel machines so as to minimize the maximum earliness or tardiness cost incurred for each of the jobs. Earliness and tardiness costs are given by general (but job-independent) functions of the amount of time a job is completed prior to or after a common due date. We show that in problems with a nonrestrictive due date, the problem decomposes into two parts. Each of the M longest jobs is assigned to a different machine, and all other jobs are assigned to the machines so as to minimize their makespan.
As the only practical way to deal with most path-dependent instruments, Monte Carlo estimation is now one of the workhorses of modern derivatives valuation. It has the advantage of being relatively easy to implement in its basic form, and, given enough computer resources, it will converge asymptotically to the correct answer. Yet, once these general principles are acknowledged, one faces the fact that many problems have such high dimension that the basic Monte Carlo technique can require an enormous number of simulations before convergence to a reasonably accurate answer is achieved.
The Monte Carlo approach has proved to be a valuable and flexible computational tool in modern finance. This paper discusses some of the recent applications of the Monte Carlo method to security pricing problems, with emphasis on improvements in efficiency. We first review some variance reduction methods that have proved useful in finance. Then we describe the use of deterministic low-discrepancy sequences, also known as quasi-Monte Carlo methods, for the valuation of complex derivative securities.
The Monte Carlo approach has proved to be a valuable and flexible computational tool in modern finance. This paper discusses some of the recent applications of the Monte Carlo method to security pricing problems, with emphasis on improvements in efficiency. We first review some variance reduction methods that have proved useful in finance. Then we describe the use of deterministic low-discrepancy sequences, also known as quasi-Monte Carlo methods, for the valuation of complex derivative securities.
We consider a general class of queueing systems with multiple job types and a flexible service facility. The arrival times and sizes of incoming jobs are random, and correlations among the sizes of arriving job types are allowed. By choosing among a finite set of configurations, the facility can dynamically control the rates at which it serves the various job types. We define system work at any given time as the minimum time required to process all jobs currently in the backlog.
We develop a simulation algorithm for estimating the prices of American-style securities, i.e., securities with opportunities for early exercise. Our algorithm provides both point estimates and error bounds for the true security price. It generates two estimates, one biased high and one biased low, both asymptotically unbiased and converging to the true price. Combining the two estimators yields a confidence interval for the true price.
We develop a simulation algorithm for estimating the prices of American-style securities, i.e., securities with opportunities for early exercise. Our algorithm provides both point estimates and error bounds for the true security price. It generates two estimates, one biased high and one biased low, both asymptotically unbiased and converging to the true price. Combining the two estimators yields a confidence interval for the true price.