Publications
30 results found
Haugh M, Caldentey R, 2024, Multi-market Cournot equilibria with heterogeneous resource-constrained firms, Operations Research, ISSN: 0030-364X
We study Cournot competition among firms in a multi-market framework where each ofthe firms face different budget / capacity constraints. We assume independent linear inversedemand functions for each market, and completely characterize the resulting unique equilibrium.Specifically, we introduce the notions of augmented and cutoff budgets for firms and markets,respectively. We show, for example, that firm i operates in market j if and only if firm i’saugmented budget is greater than market j’s cutoff budget. We also study the properties of theequilibrium as a function of the number of firms N while keeping the aggregate budget fixed.In a numerical study, we show that increasing N increases the total output across all marketsalthough this monotonicity can fail to hold at the individual market level. Similarly, we showthat that while the firms’ cumulative payoff decreases in N, the consumer surplus and socialsurplus increase in N.
Haugh M, Singal R, 2023, Counterfactual analysis in dynamic latent-state models, International Conference on Machine Learning 2023, Publisher: MLResearchPress, Pages: 12647-12677
We provide an optimization-based framework toperform counterfactual analysis in a dynamicmodel with hidden states. Our framework isgrounded in the “abduction, action, and predic-tion” approach to answer counterfactual queriesand handles two key challenges where (1) thestates are hidden and (2) the model is dynamic.Recognizing the lack of knowledge on the under-lying causal mechanism and the possibility of in-finitely many such mechanisms, we optimize overthis space and compute upper and lower boundson the counterfactual quantity of interest. Ourwork brings together ideas from causality, state-space models, simulation, and optimization, andwe apply it on a breast cancer case study. To thebest of our knowledge, we are the first to computelower and upper bounds on a counterfactual queryin a dynamic latent-state model.
Selvi A, Belbasi R, Haugh M, et al., 2022, Wasserstein logistic regression with mixed features, NeurIPS 2022, Publisher: NeurIPs, ISSN: 1049-5258
Recent work has leveraged the popular distributionally robust optimizationparadigm to combat overfitting in classical logistic regression. While the resultingclassification scheme displays a promising performance in numerical experiments,it is inherently limited to numerical features. In this paper, we show that distri-butionally robust logistic regression with mixed (i.e., numerical and categorical)features, despite amounting to an optimization problem of exponential size, ad-mits a polynomial-time solution scheme. We subsequently develop a practicallyefficient column-and-constraint approach that solves the problem as a sequence ofpolynomial-time solvable exponential conic programs. Our model retains manyof the desirable theoretical features of previous works, but—in contrast to theliterature—it does not admit an equivalent representation as a regularized logisticregression, that is, it represents a genuinely novel variant of logistic regression.We show that our method outperforms both the unregularized and the regularizedlogistic regression on categorical as well as mixed-feature benchmark instances.
Haugh M, Wang C, 2022, Play like the pros? Solving the game of darts as a dynamic zero-sum game, Informs Journal on Computing, Vol: 34, Pages: 2383-2865, ISSN: 1091-9856
The game of darts has enjoyed great growth over the past decade with the perception of darts moving from that of a pub game to a game that is regularly scheduled on prime-time television in many countries such as the United Kingdom, Germany, the Netherlands, and Australia, among others. It involves strategic interactions between two players, but to date, the literature has ignored these interactions. In this paper, we formulate and solve the game of darts as a dynamic zero-sum game (ZSG), and to the best of our knowledge, we are the first to do so. We also estimate individual skill models using a novel data set based on darts matches that were played by the top 16 professional players in the world during the 2019 season. Using the fitted skill models and our ZSG problem formulation, we quantify the importance of playing strategically—that is, taking into account the score and strategy of one’s opponent—when computing an optimal strategy. For top professionals, we find that playing strategically results in an increase in win probability of just 0.2%–0.6% over a single leg but as much as 2.2% over a best-of-31-legs match.Summary of Contribution: Dynamic zero-sum games (ZSGs) are of considerable interest, as they arise in many applications including sports, the management of communication networks, interdiction games, and heads-up poker—an important topic in modern artificial intelligence. In this study we consider the game of darts, which is growing increasingly popular around the world today. We formulate the game of darts as a ZSG and solve it iteratively by formulating each player’s best-response problem as a stochastic shortest-path (SSP) problem. We then solve these SSPs using standard dynamic programming methods. In solving the ZSG, we are able to accurately quantify the importance of top professionals playing strategically.
Haugh M, Singal R, 2021, How to play fantasy sports strategically (and win), Management Science, Vol: 67, Pages: 72-92, ISSN: 0025-1909
Daily fantasy sports (DFS) is a multibillion-dollar industry with millions of annual users and widespread appeal among sports fans across a broad range of popular sports. Building on recent work, we provide a coherent framework for constructing DFS portfolios where we explicitly model the behavior of other DFS players. We formulate an optimization problem that accurately describes the DFS problem for a risk-neutral decision maker in both double-up and top-heavy payoff settings. Our formulation maximizes the expected reward subject to feasibility constraints, and we relate this formulation to mean-variance optimization and the outperformance of stochastic benchmarks. Using this connection, we show how the problem can be reduced to the problem of solving a series of binary quadratic programs. We also propose an algorithm for solving the problem where the decision maker can submit multiple entries to the DFS contest. This algorithm is motivated by submodularity properties of the objective function and by some new results on parimutuel betting. One of the contributions of our work is the introduction of a Dirichlet-multinomial data-generating process for modeling opponents’ team selections, and we estimate the parameters of this model via Dirichlet regressions. A further benefit to modeling opponents’ team selections is that it enables us to estimate the value, in a DFS setting, of both insider trading and collusion. We demonstrate the value of our framework by applying it to DFS contests during the 2017 National Football League season.
Haugh MB, Lacedelli OR, 2020, Information Relaxation Bounds for Partially Observed Markov Decision Processes, IEEE TRANSACTIONS ON AUTOMATIC CONTROL, Vol: 65, Pages: 3256-3271, ISSN: 0018-9286
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Haugh M, Ruiz Lacedelli O, 2020, Scenario analysis for derivatives portfolios via dynamic factor models, Quantitative Finance, Vol: 20, Pages: 547-571, ISSN: 1469-7688
A classic approach to financial risk management is the use of scenario analysis to stress test portfolios. In the case of an S&P 500 options portfolio, for example, a scenario analysis might report a P&L of −$1m in the event the S&P 500 falls 5% and its implied volatility surface increases by 3 percentage points. But how accurate is this reported value of −$1m? Such a number is typically computed under the (implicit) assumption that all other risk factors are set to zero. But this assumption is generally not justified as it ignores the often substantial statistical dependence among the risk factors. In particular, the expected values of the non-stressed factors conditional on the values of the stressed factors are generally non-zero. Moreover, even if the non-stressed factors were set to their conditional expected values rather than zero, the reported P&L might still be inaccurate due to convexity effects, particularly in the case of derivatives portfolios. A further weakness of this standard approach to scenario analysis is that the reported P&L numbers are generally not back-tested so their accuracy is not subjected to any statistical tests. There are many reasons for this but perhaps the main one is that scenario analysis for derivatives portfolios is typically conducted without having a probabilistic model for the underlying dynamics of the risk factors under the physical measure P. In this paper we address these weaknesses by embedding the scenario analysis within a dynamic factor model for the underlying risk factors. Such an approach typically requires multivariate state-space models that can model the real-world behavior of financial markets where risk factors are often latent, and that are sufficiently tractable so that we can compute (or simulate from) the conditional distribution of unstressed risk factors. We demonstrate how this can be done for observable as well as latent risk factors in examples drawn from options and f
Fagan F, Haugh M, Cooper H, 2019, The advantage of lefties in one-on-one sports, Journal of Quantitative Analysis in Sports, Vol: 15, Pages: 1-25, ISSN: 1559-0410
Left-handers comprise approximately 15% of professional tennis players, but only 11% of the general population. In boxing, baseball, fencing, table-tennis and specialist batting positions in cricket the contrast is even starker, with 30% or more of top players often being left-handed. In this paper we propose a model for identifying the advantage of being left-handed in one-on-one interactive sports (as well as the inherent skill of each player). We construct a Bayesian latent ability model in the spirit of the classic Glicko model but with the additional complication of having a latent factor, i.e. the advantage of left-handedness, that we need to estimate. Inference is further complicated by the truncated nature of data-sets that arise from only having data of the top players. We show how to infer the advantage of left-handedness when only the proportion of top left-handed players is available. We use this result to develop a simple dynamic model for inferring how the advantage of left-handedness varies through time. We also extend the model to cases where we have ranking or match-play data. We test these models on 2014 match-play data from top male professional tennis players, and the dynamic model on data from 1985 to 2016.
Haugh MB, Caldentey R, 2017, A Cournot-Stackelberg Model of Supply Contracts with Financial Hedging and Identical Retailers, Foundations and Trends in Technology, Information and Operations Management, ISSN: 1571-9545
Brown DB, Haugh MB, 2017, Information Relaxation Bounds for Infinite Horizon Markov Decision Processes, Operations Research, Vol: 65, Pages: 1355-1379, ISSN: 0030-364X
Haugh M, Iyengar G, Wang C, 2016, Tax-aware dynamic asset allocation, Operations Research, Vol: 64, Pages: 849-866, ISSN: 0030-364X
We consider dynamic asset allocation problems where the agent is required to pay capital gains taxes on her investment gains. These are very challenging problems because the tax owed whenever a security is sold depends on the cost basis, and this results in high-dimensional problems, which cannot be solved exactly except in the case of very stylized problems with just one or two securities and relatively few time periods. In this paper, we focus on exact and average cost-basis problems, make the limited use of losses (LUL) assumption and develop simple heuristic trading policies for these problems when there are differential tax rates for long- and short-term gains and losses. We use information relaxation-based duality techniques to assess the performance of these trading policies by constructing unbiased lower and upper bounds on the (unknown) optimal value function. In numerical experiments with as many as 80 time periods and 25 securities we find our best suboptimal policy is within 3–10 basis points of optimality on a certainty equivalent (CE) annualized return basis. The principal contribution of this paper is in demonstrating that while the primal problem remains very challenging to solve exactly, we can easily solve very large dual problem instances. Moreover, dual tractability extends to standard problem variations, including problems with random time horizons, no wash sales constraints, intertemporal consumption and recursive utility, as well as the step-up feature of the U.S. tax code, among others.
Ahn A, Haugh M, 2015, Linear Programming and the Control of Diffusion Processes, INFORMS Journal on Computing, Vol: 27, Pages: 646-657, ISSN: 1091-9856
Haugh MB, Iyengar G, Song I, 2015, A Generalized Risk Budgeting Approach to Portfolio Construction, Journal of Computational Finance, ISSN: 1755-2850
Ahn A, Haugh M, Jain A, 2015, Consistent Pricing of Options on Leveraged ETFs, SIAM Journal on Financial Mathematics, Vol: 6, Pages: 559-593
Haugh M, Wang C, 2014, Dynamic portfolio execution and information relaxations, SIAM Journal on Financial Mathematics, Vol: 5, Pages: 316-359, ISSN: 1945-497X
We consider a portfolio execution problem where a possibly risk-averse agent needs to trade a fixed number of shares in multiple stocks over a short time horizon. Our price dynamics can capture linear but stochastic temporary and permanent price impacts as well as stochastic volatility. In general it is not possible to solve even numerically for the optimal policy in this model, however, and so we must instead search for good suboptimal policies. Our principal policy is a variant of an open-loop feedback control (OLFC) policy, and we show how the corresponding OLFC value function may be used to construct good primal and dual bounds on the optimal value function. The dual bound is constructed using the recently developed duality methods based on information relaxations. One of the contributions of this paper is the identification of sufficient conditions to guarantee convexity, and hence tractability, of the associated dual problem instances. That said, we do not claim that the only plausible models are those where all dual problem instances are convex. We also show that it is straightforward to include a nonlinear temporary price impact as well as return predictability in our model. We demonstrate numerically that good dual bounds can be computed quickly even when nested Monte Carlo simulations are required to estimate the so-called dual penalties. These results suggest that the dual methodology can be applied in many models where closed-form expressions for the dual penalties cannot be computed.
Haugh M, Lim AEB, 2012, Linear–quadratic control and information relaxations, Operations Research Letters, Vol: 40, Pages: 521-528, ISSN: 0167-6377
Chandramouli SS, Haugh MB, 2012, Erratum to “A unified approach to multiple stopping and duality” [Oper. Res. Lett. (2012)], Operations Research Letters, Vol: 40, Pages: 422-423, ISSN: 0167-6377
Chandramouli SS, Haugh MB, 2012, A unified approach to multiple stopping and duality, Operations Research Letters, Vol: 40, Pages: 258-264, ISSN: 0167-6377
Haugh MB, 2011, A note on constant proportion trading strategies, Operations Research Letters, Vol: 39, Pages: 172-179, ISSN: 0167-6377
Haugh M, Jain A, 2011, The Dual Approach to Portfolio Evaluation: A Comparison of the Static, Myopic and Generalized Buy-and-Hold Strategies, SSRN Electronic Journal, Vol: 11, Pages: 81-99, ISSN: 1469-7688
Haugh M, 2010, A Note on Constant Proportion Trading Strategies, SSRN Electronic Journal
Caldentey R, Haugh MB, 2009, Supply Contracts with Financial Hedging, Operations Research, Vol: 57, Pages: 47-65, ISSN: 0030-364X
<jats:p> We study the performance of a stylized supply chain where two firms, a retailer and a producer, compete in a Stackelberg game. The retailer purchases a single product from the producer and afterward sells it in the retail market at a stochastic clearance price. The retailer, however, is budget constrained and is therefore limited in the number of units that he may purchase from the producer. We also assume that the retailer's profit depends in part on the realized path or terminal value of some observable stochastic process. We interpret this process as a financial process such as a foreign exchange rate or interest rate. More generally, the process can be interpreted as any relevant economic index. We consider a variation (the flexible contract) of the traditional wholesale price contract that is offered by the producer to the retailer. Under this flexible contract, at t = 0 the producer offers a menu of wholesale prices to the retailer, one for each realization of the financial process up to a future time τ. The retailer then commits to purchasing at time τ a variable number of units, with the specific quantity depending on the realization of the process up to time τ. Because of the retailer's budget constraint, the supply chain might be more profitable if the retailer was able to shift some of the budget from states where the constraint is not binding to states where it is binding. We therefore consider a variation of the flexible contract, where we assume that the retailer is able to trade dynamically between zero and τ in the financial market. We refer to this variation as the flexible contract with hedging. We compare the decentralized competitive solution for the two contracts with the solutions obtained by a central planner. We also compare the supply chain's performance across the two contracts. We find, for example, that the producer always prefers the flexible contract with hedging to the flexible contract without hedging. D
Haugh MB, Kogan L, 2007, Duality Theory and Approximate Dynamic Programming for Pricing American Options and Portfolio Optimization, Handbooks in Operations Research and Management Science: Financial Engineering, Editors: Birge, Linetsky, Publisher: Elsevier, ISBN: 9780080553252
Haugh MB, Jain A, 2007, Cross-Path Regressions and Pathwise Estimators: An Application to Evaluating Portfolio Strategies, Proceedings of the 2007 Winter Simulation Conference, ISSN: 0275-0708
Haugh MB, Kogan L, Wang J, 2006, Portfolio Evaluation: A Duality Approach, Operations Research, ISSN: 0030-364X
Haugh MB, Caldentey R, 2006, Optimal Control and Hedging of Operations in the Presence of Financial Markets, Mathematics of Operations Research, ISSN: 0364-765X
Haugh MB, Kogan L, 2004, Pricing American Options: A Duality Approach, Operations Research, ISSN: 0030-364X
Haugh MB, 2003, Duality Theory and Simulation in Financial Engineering, Proceedings of the 2003 Winter Simulation Conference, ISSN: 0275-0708
Haugh MB, Lo A, 2001, Asset Allocation and Derivatives, Quantitative Finance, ISSN: 1469-7688
Haugh MB, MacHale D, 1997, The Subgroup Generated by the Squares, Proceedings of the Royal Irish Academy. Section A, Mathematical, Astronomical, and Physical Science, ISSN: 0035-8975
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