Economics and Information Theory

Stochastic programming can effectively describe many decision-making problems in uncertain environments. Unfortunately, such programs are often computationally demanding to solve. In addition, their solution can be misleading when there is ambiguity in the choice of a distribution for the random parameters. In this paper, we propose a model that describes uncertainty in both the distribution form (discrete, Gaussian, exponential, etc.) and moments (mean and covariance matrix). We demonstrate that for a wide range of cost functions the associated distributionally robust (or min-max) stochastic program can be solved efficiently. Furthermore, by deriving a new confidence region for the mean and the covariance matrix of a random vector, we provide probabilistic arguments for using our model in problems that rely heavily on historical data. These arguments are confirmed in a practical example of portfolio selection, where our framework leads to better-performing policies on the “true” distribution underlying the daily returns of financial assets.

/pdf/distributionally-robust-optimization-under-moment-4d1au1dpky.pdf

Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems

In this paper we show how to formulate and solve robust portfolio selection problems. The objective of these robust formulations is to systematically combat the sensitivity of the optimal portfolio to statistical and modeling errors in the estimates of the relevant market parameters. We introduce "uncertainty structures" for the market parameters and show that the robust portfolio selection problems corresponding to these uncertainty structures can be reformulated as second-order cone programs and, therefore, the computational effort required to solve them is comparable to that required for solving convex quadratic programs. Moreover, we show that these uncertainty structures correspond to confidence regions associated with the statistical procedures employed to estimate the market parameters. Finally, we demonstrate a simple recipe for efficiently computing robust portfolios given raw market data and a desired level of confidence.

Robust portfolio selection problems

The Price of Inequality: How Today's Divided Society Endangers Our Future. Joseph E. Stiglitz, 414 pages, New York: W. W. Norton & Company, 2012.I LOVE THESE GUYS''(Joseph Stiglitz) is an insanely great economist,'' so writes Paul R. Krugman, who should know. These two like to write books for the populace at large on the topic of macroeconomics. Krugman also likes to spout offon Sunday news shows like ''Meet the Press,'' and on all the cable news programs. You can see Krugman arguing with Bill O'Reilly on Meet the Press. From YouTube: ''Don't call me a liar, pal, that's what you do all the time,'' says O'Reilly; ''This is not your show, so you can't cut offmy mic,'' says Krugman. Judging by their expressions, I was glad Tim Russert (6- 3-) was there in the studio at the time to protect Krugman (5- 7-) (O'Reilly stands 6- 4-). Conservative pundits dislike both economists, but pretty much leave Stiglitz alone.Krugman makes it a point to stay out of government affairs. Stiglitz does just the opposite, and he sometimes gets burned. Stiglitz was part of Bill Clinton's Council of Economic Advisers and was Chief Economist for the World Bank. After much criticism of the way the International Monetary Fund (IMF) conducted lending to developing countries, he was pretty much fired from the World Bank. Comparing the two, you would have to say that Stiglitz is more the bleeding heart, while Krugman says that what he dislikes most is the dishonesty he sees in political-economic discourse. Both are champions of the common man.Since Stiglitz can make the very valid claim for being ''an insanely great economist,'' most everything he says in his books should be taken seriously. There are some real gems in this book. I especially like the perspective he lends to some of the more peculiar things that happened before, during, and after the financial crisis. People hear about these things in the news from some announcer who makes them sound like just more news-bites, but they are, after all, unprecedented (and largely absurd). Take ''robo-signing'' for instance (page 198).WHAT GOES FOR NEWSRobo-signing was part of what happened during the foreclosure process after the massive numbers of defaults of subprime mortgages. Big banks intentionally did not follow mandated law. Apart from ignoring debtors' rights, an ensuing mess followed. Robo-signing was nothing less than a blatant attempt at rewriting property law, and resulted in lying to the courts about the state of each property's title, literally hundreds of times. No bank officer was charged with a crime. By contrast, the savings and loan crisis of the 1980s led to 829 individual convictions and 650 prison sentences. Nowadays the big banks just pay fines as part of settlements where they admit no guilt, and it's just part of doing business.Take algorithmic or ''flash'' trading in the stock exchanges (page 164). These are buys and sales made in nanoseconds on the basis of extracting information from the patterns of prices and trades. Nothing like real information gathered through market research on an industry, or on a firm in a certain industry, backs up these trades. But traders swear that ''price discovery'' is happening this way, and that all this backs up the efficient markets model. So on May 6, 2010 stock prices plummeted to a point where the Dow Jones temporarily lost 10% of its value. There are reasons to believe that these trades ''make markets not just more volatile but also less 'informative' '' (page 166). Still, the talk on the street is all about efficient markets (echoing Alan Greenspan's failures at the Federal Reserve).Take failed privatizations. When electric power in California was liberalized and Enron manipulated prices and public power to its advantage, this was a story about the company's accounting practices, not about privatizing something that had no business being privatized. …

The Price of Inequality: How Today's Divided Society Endangers Our Future

Research in closed-loop supply chains (CLSCs) has grown rapidly over the last 10 years. The authors offer a critical review of influential CLSC research that takes a business economics perspective. Much of the research was inspired by practice-driven thoughtpieces, and this helped to keep research focused on relevant issues. However, CLSC research has several assumptions, such as perfect substitution between new and remanufactured products that risk becoming institutionalized. There is a strong need to carefully examine current industrial practice so that research remains focused on relevant problems. Deeper understanding of consumer perceptions of remanufactured products, product diffusion, and valuation of returned products are needed for the field to continue to add insights into developing sustainable economies.

Production and Operations Management

http://columbia.edu/~js1353/pubs/ks-fair.pdf

A solution to the random assignment problem on the full preference domain

Web Search Engines employ multiple so-called crawlers to maintain local copies of web pages. But these web pages are frequently updated by their owners, and therefore the crawlers must regularly revisit the web pages to maintain the freshness of their local copies. In this paper, we propose a two-part scheme to optimize this crawling process. One goal might be the minimization of the average level of staleness over all web pages, and the scheme we propose can solve this problem. Alternatively, the same basic scheme could be used to minimize a possibly more important search engine embarrassment level metric: The frequency with which a client makes a search engine query and then clicks on a returned url only to find that the result is incorrect. The first part our scheme determines the (nearly) optimal crawling frequencies, as well as the theoretically optimal times to crawl each web page. It does so within an extremely general stochastic framework, one which supports a wide range of complex update patterns found in practice. It uses techniques from probability theory and the theory of resource allocation problems which are highly computationally efficient -- crucial for practicality because the size of the problem in the web environment is immense. The second part employs these crawling frequencies and ideal crawl times as input, and creates an optimal achievable schedule for the crawlers. Our solution, based on network flow theory, is exact as well as highly efficient. An analysis of the update patterns from a highly accessed and highly dynamic web site is used to gain some insights into the properties of page updates in practice. Then, based on this analysis, we perform a set of detailed simulation experiments to demonstrate the quality and speed of our approach.

/pdf/optimal-crawling-strategies-for-web-search-engines-yyd3k3lvsn.pdf

Optimal crawling strategies for web search engines

We study the classical stable marriage and stable roommates problems using a polyhedral approach. We propose a new LP formulation for the stable roommates problem, which has a feasible solution if and only if the underlying roommates problem has a stable matching. Furthermore, for certain special weight functions on the edges, we construct a 2-approximation algorithm for the optimal stable roommates problem. Our technique exploits features of the geometry of fractional solutions of this formulation. For the stable marriage problem, we show that a related geometry allows us to express any fractional solution in the stable marriage polytope as a convex combination of stable marriage solutions. This also leads to a genuinely simple proof of the integrality of the stable marriage polytope.

/pdf/the-geometry-of-fractional-stable-matchings-and-its-rj17gj284p.pdf

The Geometry of Fractional Stable Matchings and its Applications

We study strategic issues in the Gale-Shapley stable marriage model. In the first part of the paper, we derive the optimal cheating strategy and show that it is not always possible for a woman to recover her women-optimal stable partner from the men-optimal stable matching mechanism when she can only cheat by permuting her preferences. In fact, we show, using simulation, that the chances that a woman can benefit from cheating are slim. In the second part of the paper, we consider a two-sided matching market found in Singapore. We study the matching mechanism used by the Ministry of Education (MOE) in the placement of primary six students in secondary schools, and discuss why the current method has limited success in accommodating the preferences of the students, and the specific needs of the schools (in terms of the "mix" of admitted students). Using insights from the first part of the paper, we show that stable matching mechanisms are more appropriate in this matching market and explain why the strategic behavior of the students need not be a major concern.

Gale-Shapley Stable Marriage Problem Revisited: Strategic Issues and Applications

We study strategic issues in the Gale-Shapley stable marriage model. In the first part of the paper, we derive the optimal cheating strategy and show that it is not always possible for a woman to recover her women-optimal stable partner from the men-optimal stable matching mechanism when she can only cheat by permuting her preferences. In fact, we show, using simulation, that the chances that a woman can benefit from cheating are slim. In the second part of the paper, we consider a two-sided matching market found in Singapore. We study the matching mechanism used by the Ministry of Education (MOE) in the placement of primary six students in secondary schools, and discuss why the current method has limited success in accommodating the preferences of the students, and the specific needs of the schools (in terms of the “mix” of admitted students). Using insights from the first part of the paper, we show that stable matching mechanisms are more appropriate in this matching market and explain why the strategic behavior of the students need not be a major concern. (Stable Marriage; Strategic Issues; Gale-Shapley Algorithm; Student Posting Exercise)

http://www.columbia.edu/~js1353/pubs/tst-ms01.pdf

Jay Sethuraman

Papers

A solution to the random assignment problem on the full preference domain

Optimal crawling strategies for web search engines

The Geometry of Fractional Stable Matchings and its Applications

Gale-Shapley Stable Marriage Problem Revisited: Strategic Issues and Applications

Gale-Shapley Stable Marriage Problem Revisited: Strategic Issues and Applications