Dual Bounds for Periodical Stochastic Programs

A construction of the dual of a periodical formulation of infinite-horizon linear stochastic programs with a discount factor is discussed. The dual problem is used for computing a deterministic upper bound for the optimal value of the considered multistage stochastic program. Numerical experiments demonstrate behavior of that upper bound, especially when the discount factor is close to one.

Consistency Cuts for Dantzig-Wolfe Reformulations

A New Family of Valid-Inequalities for Dantzig-Wolfe Reformulation of Mixed Integer Linear Programs In “Consistency Cuts for Dantzig-Wolfe Reformulation,” Jens Vinther Clausen, Richard Lusby, and Stefan Ropke present a new family of valid inequalities to be applied to Dantzig-Wolfe reformulations with binary linking variables. They show that, for Dantzig-Wolfe reformulations of mixed integer linear programs that satisfy certain properties, it is enough to solve the linear programming relaxation of the Dantzig-Wolfe reformulation with all consistency cuts to obtain integer solutions. An example of this is the temporal knapsack problem; the effectiveness of the cuts is tested on a set of 200 instances of this problem, and the results are state-of-the-art solution times. For problems that do not satisfy these conditions, the cuts can still be used in a branch-and-cut-and-price framework. In order to show this, the cuts are applied to a set of generic mixed linear integer programs from the online library MIPLIB. These tests show the applicability of the cuts in general.

Cross-Sectional Variation of Intraday Liquidity, Cross-Impact, and Their Effect on Portfolio Execution

Over the past decade, there has been a significant rise in assets managed under passive and systematic strategies. Such strategies hold and trade portfolios in a coordinated manner, often concentrating trading around the end of the trading session. Simultaneously, there has been a rise in activity from market participants that act as liquidity providers, themselves trading along portfolio directions. In “Cross-Sectional Variation of Intraday Liquidity, cross-impact, and Their Effect on Portfolio Execution,” Min, Maglaras, and Moallemi investigate the implications of these two observations, specifically exploring how the phenomenon of portfolio liquidity provision leads to cross-security impact and influences the optimal execution schedules of risk-neutral traders that seek to minimize their expected execution costs. They show that the optimized schedules deviate from the naïve approach that trades each security separately and instead, couple the trading intensity across stocks so as to benefit from the liquidity provided along attractive portfolio trading directions. Empirical analysis demonstrates that coupled optimized schedules could lower costs by as much as 15% relative to the naïve approach.

Extremizing and Antiextremizing in Bayesian Ensembles of Binary-Event Forecasts

Many organizations combine forecasts of probabilities of binary events to support critical business decisions, such as the approval of credit or the recommendation of a drug. To aggregate individual probabilities, we offer a new method based on Bayesian principles that can help identify why and when combined probabilities need to be extremized. Extremizing is typically viewed as shifting the average probability farther from one half; we emphasize that it is more suitable to define extremizing as shifting it farther from the base rate. We introduce the notion of antiextremizing, cases in which it might be beneficial to make average probabilities less extreme. Analytically, we find that our Bayesian ensembles often extremize the average forecast but sometimes antiextremize instead. On several publicly available data sets, we demonstrate that our Bayesian ensemble performs well and antiextremizes anywhere from 18% to 73% of the cases. Antiextremizing is required more often when there is bracketing with respect to the base rate among the probabilities being aggregated than with no bracketing.

Weighted Scoring Rules and Convex Risk Measures

In Weighted Scoring Rules and Convex Risk Measures, Dr. Zachary J. Smith and Prof. J. Eric Bickel (both at the University of Texas at Austin) present a general connection between weighted proper scoring rules and investment decisions involving the minimization of a convex risk measure. Weighted scoring rules are quantitative tools for evaluating the accuracy of probabilistic forecasts relative to a baseline distribution. In their paper, the authors demonstrate that the relationship between convex risk measures and weighted scoring rules relates closely with previous economic characterizations of weighted scores based on expected utility maximization. As illustrative examples, the authors study two families of weighted scoring rules based on phi-divergences (generalizations of the Weighted Power and Weighted Pseudospherical Scoring rules) along with their corresponding risk measures. The paper will be of particular interest to the decision analysis and mathematical finance communities as well as those interested in the elicitation and evaluation of subjective probabilistic forecasts.

Systemic Risk-Driven Portfolio Selection

How can we construct portfolios that perform well in the face of systemic events? The global financial crisis of 2007–2008 and the coronavirus disease 2019 pandemic have highlighted the importance of accounting for extreme form of risks. In “Systemic Risk-Driven Portfolio Selection,” Capponi and Rubtsov investigate the design of portfolios that trade off tail risk and expected growth of the investment. The authors show how two well-known risk measures, the value-at-risk and the conditional value-at-risk, can be used to construct portfolios that perform well in the face of systemic events. The paper uses U.S. stock data from the S&P500 Financials Index and Canadian stock data from the S&P/TSX Capped Financial Index, and it demonstrates that portfolios accounting for systemic risk attain higher risk-adjusted expected returns, compared with well-known benchmark portfolio criteria, during times of market downturn.

The Gatekeeper’s Dilemma: “When Should I Transfer This Customer?”

When Should I Transfer This Customer? “Please hold while I transfer you to next level of support.” Most of us have been on the receiving end of this message. In this study, the authors look at transfers from the service worker’s perspective. They create an online experiment in which participants play the role of call center agents who need to decide whether to transfer a virtual service request or continue attempting to resolve it. Consistent with compensation schemes common in call centers, participants receive a bonus for each successful resolution and may pay a penalty if they transfer. The authors find that these incentives generally work well; however, agents appear to overreact to transfer penalties by handling more requests than they should and transferring too few requests. Although this may be good news for customers who dislike being transferred, such behaviors may be costly for the call center; thus, managers need to be careful when rolling out complex compensation schemes.

Shortfall Risk Models When Information on Loss Function Is Incomplete

Utility-based shortfall risk measures effectively captures a decision maker's risk attitude on tail losses. In this paper, we consider a situation where the decision maker's risk attitude toward tail losses is ambiguous and introduce a robust version of shortfall risk, which mitigates the risk arising from such ambiguity. Specifically, we use some available partial information or subjective judgement to construct a set of plausible utility-based shortfall risk measures and define a so-called preference robust shortfall risk as through the worst risk that can be measured in this (ambiguity) set. We then apply the robust shortfall risk paradigm to optimal decision-making problems and demonstrate how the latter can be reformulated as tractable convex programs when the underlying exogenous uncertainty is discretely distributed.

Objective Selection for Cancer Treatment: An Inverse Optimization Approach

The quality of radiation therapy treatment plans and the efficiency of the planning process are heavily affected by the choice of planning objectives. Although simple objectives enable efficient treatment planning, the resulting treatment quality might not be clinically acceptable; complex objectives can generate high-quality treatment, yet the planning process becomes computationally prohibitive. In “Objective Selection for Cancer Treatment: An Inverse Optimization Approach,” by integrating inverse optimization and feature selection techniques, Ajayi, Lee, and Schaefer propose a novel objective selection method that uses historical radiation therapy treatment data to infer a set of planning objectives that are tractable and parsimonious yet clinically effective. Although the objective selection problem is a large-scale bilevel mixed-integer program, the authors propose various solution approaches inspired by feature selection greedy algorithms and patient-specific anatomical characteristics.

Actor-Critic–Like Stochastic Adaptive Search for Continuous Simulation Optimization

Many systems arising in applications from engineering design, manufacturing, and healthcare require the use of simulation optimization (SO) techniques to improve their performance. In “Actor-Critic–Like Stochastic Adaptive Search for Continuous Simulation Optimization,” Q. Zhang and J. Hu propose a randomized approach that integrates ideas from actor-critic reinforcement learning within a class of adaptive search algorithms for solving SO problems. The approach fully retains the previous simulation data and incorporates them into an approximation architecture to exploit knowledge of the objective function in searching for improved solutions. The authors provide a finite-time analysis for the method when only a single simulation observation is collected at each iteration. The method works well on a diverse set of benchmark problems and has the potential to yield good performance for complex problems using expensive simulation experiments for performance evaluation.