Informs 2015

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INFORMS Philadelphia – 2015
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SA08
SA06
06-Room 306, Marriott
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,
1 - Robust Dynamic Optimization of Credit Portfolios
Agostino Capponi, Columbia, Mudd 313, New York, NY, 10027,
United States of America,
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, , 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,
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, ,
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,
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,
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.
2 - Optimal Static Quadratic Hedging
Tim Leung, Professor, Columbia University, 116th Street, New
York, NY, 10027, United States of America,
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,
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, , 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,
1 - A Robust Optimization Approach for Identifying Disruptive Nodes
in Networks
Joe Naoum-sawaya, IBM Research, Damastown Industrial Estate,
Dublin 15, Ireland, ,
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,
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, , 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.