Raymond McKendall

A stochastic programming model for money management

Abstract Portfolio managers in the new fixed-income securities have to cope with various forms of uncertainty, in addition to the usual interest rate changes. Uncertainy in the timing and amount of cashflows, changes in the default and other risk premia and so on, complicate the portfolio managers problem. We develop here a multi-period, dynamic, portfolio optimization model to address this problem. The model specifies a sequence of investment decisions over time that maximize the expected utility of return at the end of the planning horizon. The model is a two-stage stochastic program with recourse. The dynamics of interest rates, cashflow uncertainty, and liquidity, default and other risk premia, are explicitly modeled through postulated scenarios. Simulation procedures are developed to generate these scenarios. The optimization models are then integrated with the simulation procedures. Extensive validation experiments are carried out to establish the effectiveness of the model in dealing with uncertainty. In particular the model is compared against the popular portfolio immunization strategy, and against a portfolio based on mean-absolute deviation optimization.

Robust fusion of location information

A sensor fusion problem for location data using statistical decision theory (SDT) is studied. The contribution of this study is the application of SDT to obtain a robust test of the hypothesis that data from different sensors is consistent and a robust procedure for combining the date which pass this preliminary consistency test. Here, robustness refers to the statistical effectiveness of the decision rules when the probability distributions of the observation noise and the a priori position information associated with the individual sensors are uncertain. Location data refers to observations of the form Z= theta +V, where V represents additive sensor noise and theta denotes the sensed parameter of interest to the observer. The paper focuses on epsilon -contamination models, which allow one to account for heavy-tailed deviations from nominal sampling distributions.<<ETX>>

Real-time 3D-teleimmersion

In this paper we present the first implementation of a new medium for telecollaboration. The realized testbed consists of two tele-cubicles at two Internet nodes. At each telecubicle a stereo-rig is used to provide an accurate dense 3D-reconstruction of a person in action. The two real dynamic worlds are transmitted over the network and visualized stereoscopically. The full-3D information facilitates interaction with any virtual object, demonstrating in an optimal way the confluence of graphics, vision, and communication.

Computing Price Paths of Mortgage-Backed Securities Using Massively Parallel Computing

We consider the problem of pricing fixed-rate mortgage-backed securities (abbreviated: MBS). In particular, we develop a model that tracks the price of MBS across time, but also under different scenarios of the term structure. Central to the developments of this paper is the use of massively parallel computing technology. The computational complexities of MBS, and the related pricing model, rendered them intractable on current workstations or large mainframes. The paper also develops practical procedures for the computation of the pricing model on massively parallel systems, like the Connection Machine CM—2.

Stochastic Programming Models for Portfolio Optimization with Mortgage Backed Securities: Comprehensive Research Guide

This research develops mathematical models for an investment problem in asset-liability management of complex fixed-income securities under uncertainty. The specific problem is to fund a known liability with a portfolio of mortgage-backed securities in an uncertain interest-rate environment, but the approach considered extends easily to include other fixed-income investments and other types of uncertainty. The mathematical models are multi-stage stochastic programs based on multiple scenarios of horizon analysis of the candidate securities. The main contributions of this research are its formulation, application, and evaluation of multi-stage stochastic programming for fixed-income management. Secondary contributions include implementation of horizon analysis and integration of horizon analysis and stochastic programming. This report is a comprehensive guide to the design and evaluation of the models.

Using robust statistics for sensor fusion

The purpose of this article is to describe research in sensor fusion with statistical decision theory in the GRASP Lab, Department of Computer and Information Science, University of Pennsylvania. This article is thus a tutorial overview of the general research problem, the mathematical framework for the analysis, and the results of specific research problems. The intended audience for this article is a reader seeking a self-contained summary of the research. The prerequisite for understanding this article is familiarity with basic mathematical statistics.

Multivariate data fusion based on fixed-geometry confidence sets

The successful design and operation of autonomous or partially autonomous vehicles which are capable of traversing uncertain terrains requires the application of multiple sensors for tasks such as: local navigation, terrain evaluation, and feature recognition. In applications which include a teleoperation mode, there remains a serious need for local data reduction and decision-making to avoid the costly or impractical transmission of vast quantities of sensory data to a remote operator. There are several reasons to include multi-sensor fusion in a system design: (i) it allows the designer to combine intrinsically dissimilar data from several sensors to infer some property or properties of the environment, which no single sensor could otherwise obtain; and (ii) it allows the system designer to build a robust system by using partially redundant sources of noisy or otherwise uncertain information. At present, the epistemology of multi-sensor fusion is incomplete. Basic research topics include the following taskrelated issues: (i) the value of a sensor suite; (ii) the layout, positioning, and control of sensors (as agents); (iii) the marginal value of sensor information; the value of sensing-time versus some measure of error reduction, e.g., statistical efficiency; (iv) the role of sensor models, as well as a priori models of the environment; and (v) the calculus or calculi by which consistent sensor data are determined and combined. In our research on multi-sensor fusion, we have focused our attention on several of these issues. Specifically, we have studied the theory and application of robust fixed-size confidence intervals as a methodology for robust multi-sensor fusion. This work has been delineated and summarized in Kamberova and Mintz (1990) and McKendall and Mintz (1990a, 1990b). As we noted, this previous research focused on confidence intervals as opposed to the more general paradigm of confidence sets. The basic distinction here is between fusing data characterized by an uncertain scalar parameter versus fusing data characterized by an uncertain vector parameter, of known dimension. While the confidence set paradigm is more widely applicable, we initially chose to address the confidence interval paradigm, since we were simultaneously interested in addressing the issues of: (i) robustness to nonparametric uncertainty in the sampling distribution; and (ii) decision procedures for small sample sizes. Recently, we have begun to investigate the multivariate (confidence set) paradigm. The delineation of optimal confidence sets with fixed geometry is a very challenging problem when: (i) the a priori knowledge of the uncertain parameter vector is not modeled by a Cartesian product of intervals (a hyper-rectangle); and/or (ii) the noise components in the multivariate observations are not statistically independent. Although it may be difficult to obtain optimal fixed-geometry confidence sets, we have obtained some very promising approximation techniques. These approximation techniques provide: (i) statistically efficient fixed-size hyper-rectangular confidence sets for decision models with hyper-ellipsoidal parameter sets; and (ii) tight upper and lower bounds to the optimal confidence coefficients in the presence of both Gaussian and non-Gaussian sampling distributions. In both the univariate and multivariate paradigms, it is assumed that the a priori uncertainty in the parameter value can be delineated by a fixed set in an n-dimensional Euclidean space. It is further assumed, that while the sampling distribution is uncertain, the uncertainty class description for this distribution can be delineated by a given class of neighborhoods in the space of all n-dimensional probability distributions. The following sections of this paper: (i) present a paradigm for multi-sensor fusion based on position data; (ii) introduce statistical and set-valued models for sensor errors and a priori environmental uncertainty; (iii) explain the role of confidence sets in statistical decision theory and sensor fusion; (iv) relate fixed-size confidence intervals to fixedgeometry confidence sets; and (v) examine the performance of fixed-size hyper-cubic confidence sets for decision models with spherical parameter sets in the presence of both Gaussian and non-Gaussian sampling distributions