Ciamac C. Moallemi

An Axiomatic Approach to Systemic Risk

Systemic risk refers to the risk of collapse of an entire complex system as a result of the actions taken by the individual component entities or agents that comprise the system. Systemic risk is an issue of great concern in modern financial markets as well as, more broadly, in the management of complex business and engineering systems. We propose an axiomatic framework for the measurement and management of systemic risk based on the simultaneous analysis of outcomes across agents in the system and over scenarios of nature. Our framework defines a broad class of systemic risk measures that accomodate a rich set of regulatory preferences. This general class of systemic risk measures captures many specific measures of systemic risk that have recently been proposed as special cases and highlights their implicit assumptions. Moreover, the systemic risk measures that satisfy our conditions yield decentralized decompositions; i.e., the systemic risk can be decomposed into risk due to individual agents. Furthermore, one can associate a shadow price for systemic risk to each agent that correctly accounts for the externalities of the agents individual decision making on the entire system. This paper was accepted by Gerard P. Cachon, stochastic models and simulation.

Convergence of Min-Sum Message Passing for Quadratic Optimization

We establish the convergence of the min-sum message passing algorithm for minimization of a quadratic objective function given a convex decomposition. Our results also apply to the equivalent problem of the convergence of Gaussian belief propagation.

Efficient Risk Estimation via Nested Sequential Simulation

We analyze the computational problem of estimating financial risk in a nested simulation. In this approach, an outer simulation is used to generate financial scenarios, and an inner simulation is used to estimate future portfolio values in each scenario. We focus on one risk measure, the probability of a large loss, and we propose a new algorithm to estimate this risk. Our algorithm sequentially allocates computational effort in the inner simulation based on marginal changes in the risk estimator in each scenario. Theoretical results are given to show that the risk estimator has a faster convergence order compared to the conventional uniform inner sampling approach. Numerical results consistent with the theory are presented. This paper was accepted by Gerard Cachon, stochastic models and simulation.

Classifying cells for cancer diagnosis using neural networks

A computer-based system for diagnosing bladder cancer is described. Typically, an object falls into one of two classes: Well or Not-well. The Well class contains the cells that will actually be useful for diagnosing bladder cancer; the Not-well class includes everything else. Several descriptive features are extracted from each object in the image and then fed to a multilayer perceptron, which classifies them as Well or Not-well. The perceptrons superior classification abilities reduces the number of computer misclassification errors to a level tolerable for clinical use. Also, the perceptrons parallelism and other aspects of this implementation lend it to extremely fast computation, thus providing accurate classification at an acceptable speed.<<ETX>>

Protein family annotation in a multiple alignment viewer

SUMMARY The Pfaat protein family alignment annotation tool is a Java-based multiple sequence alignment editor and viewer designed for protein family analysis. The application merges display features such as dendrograms, secondary and tertiary protein structure with SRS retrieval, subgroup comparison, and extensive user-annotation capabilities. AVAILABILITY The program and source code are freely available from the authors under the GNU General Public License at http://www.pfizerdtc.com

Pathwise Optimization for Optimal Stopping Problems

We introduce the pathwise optimization (PO) method, a new convex optimization procedure to produce upper and lower bounds on the optimal value (the “price”) of a high-dimensional optimal stopping problem. The PO method builds on a dual characterization of optimal stopping problems as optimization problems over the space of martingales, which we dub the martingale duality approach. We demonstrate via numerical experiments that the PO method produces upper bounds of a quality comparable with state-of-the-art approaches, but in a fraction of the time required for those approaches. As a by-product, it yields lower bounds (and suboptimal exercise policies) that are substantially superior to those produced by state-of-the-art methods. The PO method thus constitutes a practical and desirable approach to high-dimensional pricing problems. Furthermore, we develop an approximation theory relevant to martingale duality approaches in general and the PO method in particular. Our analysis provides a guarantee on the quality of upper bounds resulting from these approaches and identifies three key determinants of their performance: the quality of an input value function approximation, the square root of the effective time horizon of the problem, and a certain spectral measure of “predictability” of the underlying Markov chain. As a corollary to this analysis we develop approximation guarantees specific to the PO method. Finally, we view the PO method and several approximate dynamic programming methods for high-dimensional pricing problems through a common lens and in doing so show that the PO method dominates those alternatives. This paper was accepted by Wei Xiong, stochastic models and simulation.

Convergence of Min-Sum Message-Passing for Convex Optimization

We establish that the min-sum message-passing algorithm and its asynchronous variants converge for a large class of unconstrained convex optimization problems, generalizing existing results for pairwise quadratic optimization problems. The main sufficient condition is that of scaled diagonal dominance. This condition is similar to known sufficient conditions for asynchronous convergence of other decentralized optimization algorithms, such as coordinate descent and gradient descent.

Approximate Dynamic Programming via a Smoothed Linear Program

We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural “projection” of a well-studied linear program for exact dynamic programming. Such programs restrict attention to approximations that are lower bounds to the optimal cost-to-go function. Our program---the “smoothed approximate linear program”---is distinct from such approaches and relaxes the restriction to lower bounding approximations in an appropriate fashion while remaining computationally tractable. Doing so appears to have several advantages: First, we demonstrate bounds on the quality of approximation to the optimal cost-to-go function afforded by our approach. These bounds are, in general, no worse than those available for extant LP approaches and for specific problem instances can be shown to be arbitrarily stronger. Second, experiments with our approach on a pair of challenging problems (the game of Tetris and a queueing network control problem) show that the approach outperforms the existing LP approach (which has previously been shown to be competitive with several ADP algorithms) by a substantial margin.

Dynamic Portfolio Choice with Linear Rebalancing Rules

We consider a broad class of dynamic portfolio optimization problems that allow for complex models of return predictability, transaction costs, trading constraints, and risk considerations. Determining an optimal policy in this general setting is almost always intractable. We propose a class of linear rebalancing rules and describe an efficient computational procedure to optimize with this class. We illustrate this method in the context of portfolio execution and show that it achieves near optimal performance. We consider another numerical example involving dynamic trading with mean-variance preferences and demonstrate that our method can result in economically large benefits.

Risk Estimation via Regression

We introduce a regression-based nested Monte Carlo simulation method for the estimation of financial risk. An outer simulation level is used to generate financial risk factors and an inner simulation level is used to price securities and compute portfolio losses given risk factor outcomes. The mean squared error (MSE) of standard nested simulation converges at the rate k −2/3 , where k measures computational effort. The proposed regression method combines information from different risk factor realizations to provide a better estimate of the portfolio loss function. The MSE of the regression method converges at the rate k −1 until reaching an asymptotic bias level which depends on the magnitude of the regression error. Numerical results consistent with our theoretical analysis are provided and numerical comparisons with other methods are also given.