2016 INFORMS Annual Meeting Program

TD41

INFORMS Nashville – 2016

TD39 207A-MCC Applied Probability and Optimization III Sponsored: Applied Probability Sponsored Session Chair: Chaitanya Bandi, c-bandi@kellogg.northwestern.edu 1 - Adaptive Control Of Flexible Queueing Networks Yuan Zhong, Columbia University, New York, NY, 10027, United States, yz2561@columbia.edu, Ramtin Pedarsani, Jean Walrand We consider the problem of designing adaptive control policies for queueing networks with flexible servers of overlapping capabilities. We show that a simple, adaptive version of the classical maxweight policy can lead to system instability. We then provide tight characterizations for systems that are stable under the simple, adaptive maxweight policy. Finally, we propose class of adaptive control policies that are throughput optimal for general parallel server systems. 2 - Delay Performance Of Scheduling Algorithms For Data Center Networks And Input Queued Switches Sivateja Maguluri, IBM, siva.theja@gmail.com Today’s era of cloud computing is powered by massive data centers hosting servers that are connected by high speed networks. It is therefore desirable to design scheduling algorithms for data packets that have low computational complexity and result in small average packet delays. We consider the scheduling problem in an input-queued switch, which is a good abstraction for a data center network. We present low complexity scheduling algorithms that have optimal queue length (equivalently, delay) behavior in the heavy traffic regime. We also present bounds on the queue length in light traffic. These results are obtained using drift based arguments. 3 - Characterizing Global Stability Of Queueing Networks Via Robust Optimization Chaithanya Bandi, Northwestern University, Evanston, IL, United States, c-bandi@kellogg.northwestern.edu, Itai Gurvich We study the conditions of global stability in open multi-class queueing networks, that is stability under any work conserving policy. We propose a new approach, where rather than aiming at the full characterization of global stability, we seek toidentify assembly (LEGO) operations, such as pooling of networks, and assembly rules-of-thumb that, when followed, crate a globally stable network from globally stable building blocks. We also use robust optimization as a key methodology that brings a new perspective to known results on global stability, state space collapse and the network Skorohod problem. 4 - Using Robust Queueing To Expose The Impact Of Dependence In Single Server Queues Wei You, PhD Student, Columbia University, 500 W. 120th St., Mudd 323, New York, NY, 10027, United States, wy2225@columbia.edu, Ward Whitt Queueing applications often exhibit dependence among interarrival times and service times, e.g., when there are multiple customer classes with class-dependent service-time distributions, or when arrivals are departures or overflows from other queues or superpositions of such complicated processes. In this talk, we show that the robust queueing approach proposed by Bandi et al. can be extended to describe the impact of dependence structure on customer waiting times and the remaining workload in service time as a function of the traffic intensity. Thus, robust queueing can be useful to develop performance approximations for queueing networks and other complex queueing systems.

2 - Synchronization Of Discrete Pulse-coupled Oscillators David Sivakoff, Ohio State University, dsivakoff@stat.osu.edu We introduce a discrete state, discrete time model of inhibitory oscillators, and analyze the long time behavior of a system of oscillators located on the integer lattice. We show that, when started from random initial condition, the system clusters (weakly synchronizes), and give upper and lower bounds on the clustering rate. 3 - Sample Path Large Deviations For Heavy Tailed Levy Processes And Their Applications Chang-Han Rhee, CWI, C.Rhee@cwi.nl While the theory of large deviations has been wildly successful in providing systematic tools for studying rare events, the central ideas behind the classical large deviations theory critically hinge on the assumption that the underlying uncertainties are light-tailed. As a result, the heavy-tailed counterparts have remained significantly less mature. In this talk, we introduce a new large deviations result for heavy-tailed Levy processes, which enables systematic study of the rare events associated with multiple big jumps, beyond the celebrated “principle of one big jump.” We illustrate the implications of the new theory in applications in computational finance and stochastic networks. TD41 207C-MCC Quantitative Methods in Finance Sponsored: Financial Services Sponsored Session Chair: Qi Wu, Chinese University of Hong Kong, Hong Kong, Shatin, NT, 12345, Hong Kong, qwu@se.cuhk.edu.hk 1 - Option Pricing In The Presence Of Market Microstructure Nan Chen, Chinese University of Hong Kong, nchen@se.cuhk.edu.hk No-arbitrage prices of vanilla options becomes nontrivial when the underlying dynamic is modeled at the order book level. By taking into account the market microstructure such as market depth and resilience, we formulate the traditional option pricing problem as a singular-impulsive control problem. Our analysis demonstrates that the liquidity-related microstructure has a profound impact on the resulting prices. 2 - On The Measurement Of Economic Tail Risk Xianhua Peng, Hong Kong University of Science & Technology, maxhpeng@ust.hk, Steven Kou This paper attempts to provide a decision-theoretic foundation for the measurement of economic tail risk, which is not only closely related to utility theory but also relevant to statistical model uncertainty. The main result is that the only risk measures that satisfy a set of economic axioms for the Choquet expected utility and the statistical property of general elicitability (i.e. there exists an objective function such that minimizing the expected objective function yields the risk measure) are the mean functional and Value-at-Risk (VaR), in particular the median shortfall, which is the median of tail loss distribution and is also the VaR at a higher confidence level. 3 - Persistence And Procyclicality In Margin Requirements Qi Wu, Chinese University of Hong Kong, qwu@se.cuhk.edu.hk Derivatives central counterparties (CCP) impose margin requirements on their clearing members to protect the CCP from the default of a member firm. A spike in volatility leads to margin calls in times of market stress. Risk-sensitive margin requirements are procyclical in the sense that they amplify shocks. We analyze how much higher margin levels need to be to avoid procyclicality. Our analysis compares the tail decay of conditional and unconditional loss distributions to compare stable and risk-sensitive margin requirements. Greater persistence in volatility leads to a slower decay in the tail of the unconditional distribution and a higher bu er needed to avoid procyclicality. 4 - Over-the Counter Markets andCounterparty Risk Agostino Capponi, Columbia University, ac3827@columbia.edu We develop a parsimonious model to study how counterparty risk influences the structure of OTC markets. A unit continuum of traders, who are risk-averse agents with exponential utility, are organized into banks. Traders of a bank strategically engage in bilateral transactions with traders of another bank taking into account the terms of deal and counterparty risk. We show that the rise of counterparty risk leads to a higher concentration of dealers.

TD40 207B-MCC Applications in Applied Probability Sponsored: Applied Probability Sponsored Session

Chair: Kevin Leder, University of Minnesota, 111 Church St, Minneapolis, MN, 55455, United States, kevinleder@gmail.com 1 - A Stochastic Model Of Order Book Dynamics Using Bouncing Geometric Brownian Motions Xin Liu, Clemson University, xliu9@clemson.edu In a limit order book, market ask price is always greater than market bid price, and these prices move upwards and downwards due to new arrivals, market trades, and cancellations. We model the two price processes as “bouncing geometric Brownian motions (GBMs)”, which are defined as exponentials of two mutually reflected Brownian motions (BM). We then modify these bouncing GBMs to construct a discrete time stochastic process of trading times and trading prices, which is parameterized by a parameter c > 0. It is shown that the logarithmic trading price process, under a suitable scaling, converges to a standard BM, and the modified ask and bid price processes approach the original bouncing GBMs, as c goes to 0.

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