# 2015 Informs Annual Meeting

SA08

INFORMS Philadelphia – 2015

SA06 06-Room 306, Marriott

2 - Optimal Static Quadratic Hedging Tim Leung, Professor, Columbia University, 116th Street, New York, NY, 10027, United States of America, tl2497@columbia.edu We propose a flexible framework for hedging European or path-dependent derivatives by holding static positions in vanilla European calls, puts, bonds, and forwards. A model-free expression is derived for the optimal static hedging strategy that minimizes the expected squared hedging error subject to a cost constraint. The versatility of our approach is illustrated through a series of examples. 3 - The Martingale Extraction Method with Applications to Long-term Cash Flows Hyungbin Park, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA, 01609, United States of America, hpark@wpi.edu The martingale extraction method is dicussed with applications. We determine the exponential decay (or growth) rate of long-term cash flows and, as one of examples, long-dated leveraged ETFs are analyzed. We then explore a sensitivity analysis with respect to perturbations in the underlying process. The method of Fournie is combined with the martingale extraction to analyze the sensitivity. 4 - Drawdown-Based Measures of Risk Olympia Hadjiliadis, Professor, Brooklyn College and the Graduate Center CUNY, 32 Willow Place, Apt. 3, Brooklyn, NY, 11201, olympia.hadjiliadis@gmail.com, Hongzhong Zhang, Tim Leung, Chris Knaplund Common risk measures, such as value-at-risk and conditional value-at-risk, are based on the distribution of terminal returns, and do not incorporate path dependence of returns. The drawdown process can be used to describe the path- wise risk – it is defined as the difference between the running maximum and the current position of a process. We define and discuss the risk measures drawdown- at-risk, conditional drawdown-at-risk, maximum drawdown-at-risk and the co-drawdown-at-risk. SA08 08-Room 308, Marriott Node Location, Node Disruption and Routing Sponsor: Telecommunications Sponsored Session Chair: Timothy Matis, Professor, Texas Tech University, 2500 Broadway, Texas, United States of America, Timothy.Matis@ttu.edu 1 - A Robust Optimization Approach for Identifying Disruptive Nodes in Networks Joe Naoum-sawaya, IBM Research, Damastown Industrial Estate, Dublin 15, Ireland, jnaoumsa@uwaterloo.ca, Christoph Buchheim The critical node selection problem (CNP) has important applications in telecommunication, supply chain design, and disease propagation prevention. In practice the weights on the connections are uncertain. Thus robust optimization approaches have been considered. In this presentation, we address general uncertainty sets and propose an exact approach based on Benders decomposition. In particular, we can deal with discrete scenario based uncertainty, gamma uncertainty, and ellipsoidal uncertainty. 2 - Location of Wireless Mobile Relays David Shallcross, Applied Communication Sicneces, 150 Mt Airy Road, Basking Ridge, NJ, 07920, United States of America, dfs@jhu.edu We consider the placement of wireless mobile relays to enable communication between clients, focusing on minimizing the maximum link length in the resulting network. We present new bounds and complexity results for the centralized problem, and analysis of an algorithm distributed among the relays themselves. 3 - A Game-Theoretic Model of Network Routing under Strategic Link Disruptions Mathieu Dahan, Master Student, Massachusetts Institute of Technology, 70 Pacific Street #648C, Cambridge, MA, 02139, United States of America, mdahan@mit.edu, Saurabh Amin We consider a network security game where the defender routes flow through a network and the attacker disrupts one or more links. The defender (resp. attacker) faces disutility (resp. utility) of lost flow, and incurs transportation cost (resp. cost of attack). We show that, under certain conditions, Nash equilibria of this game can be characterized by max-flow and min-cut of the network. We study equilibrium structure in terms of the player valuations of effective flow and the incurred costs.

Financial Engineering Sponsor: Financial Services Sponsored Session

Chair: Abel Cadenillas, Professor, University of Alberta, Department of Mathematical Sciences, Central Academic Building 632, Edmonton, AB, T6G2G1, Canada, abel@ualberta.ca 1 - Robust Dynamic Optimization of Credit Portfolios Agostino Capponi, Columbia, Mudd 313, New York, NY, 10027, United States of America, ac3827@columbia.edu We introduce a dynamic credit portfolio framework where optimal investment strategies are robust against misspecifications of the reference credit model. We provide an explicit characterization of the optimal robust bond investment strategy, in terms of default state dependent value functions associated with the max-min robust optimization criterion. The value functions can be obtained as the solutions of a recursive system of HJB differential equations. 2 - Optimal Investment and Liability Ratio Policies in a Multidimensional Regime Switching Model Abel Cadenillas, Professor, University of Alberta, Department of Mathematical Sciences, Central Academic Building 632, Edmonton, AB, T6G2G1, Canada, abel@ualberta.ca, Bin Zou We consider an insurer who faces an external jump-diffusion risk that is negatively correlated with the capital returns in a multidimensional regime switching model. The insurer selects investment and liability ratio policies continuously to maximize her/his expected utility of terminal wealth. We obtain explicit solutions for optimal investment and liability ratio policies for logarithmic, power, and exponential utility functions. 3 - Dynamic Programming in Mathematical Finance Alain Bensoussan, Professor, The University of Texas at Dallas, United States of America, axb046100@utdallas.edu Mathematical Finance has introduced new type of stochastic control problems. In this context, the martingale method has been used to solve them. This gives the impression that probabilistic techniques are the only way to obtain a solution. We show that purely analytical techniques can be used for the same result. Not only it is useful to have additional techniques, but also analytical techniques allow for more constructive solutions. We will discuss the main techniques, and give examples. 4 - A Data-driven Perspective on Transaction Costs in Portfolio Selection Victor Demiguel, Professor, London Business School, Regent’s Park, London, United Kingdom, avmiguel@london.edu, Alba V. Olivares-nadal We show that a transaction cost term can result in portfolios that are robust with respect to estimation error. Theoretically, we show that the problem with transaction costs is equivalent to: a robust portfolio problem, a robust regression problem, and a Bayesian portfolio problem. Empirically, we propose a data-driven approach to portfolio selection with transaction costs. We demonstrate using five empirical datasets that the proposed data-driven portfolios perform well out of sample.

SA07 07-Room 307, Marriott Quantitative Financial Risk Management Cluster: Risk Management Invited Session

Chair: Tim Leung, Professor, Columbia University, 116th Street, New York, NY, 10027, United States of America, tl2497@columbia.edu 1 - A Limit Order Book Model for Small-tick Stocks Xinyun Chen, Stony Brook University, Math Tower, B148 #4, New York, United States of America, xinyun.chen@stonybrook.edu, Jose Blanchet, Yanan Pei We construct a limit order book model to inform the joint evolution of the spread and the price processes for small-tick stocks. Under the multi-scale asymptotic regime suggested by empirical observations, we solve the price return distribution in terms of the order flow rates. We test our model using US stock market data. Under different scaling regimes, with respect to the autocorrelation of order flows, our results leads to different jump-diffusion models for the price dynamics.

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