Asset Substitution and Structured Financing

Suppose that a road network model is given, together with some given demand for travel by (say) car and that the demand for travel varies with time of day but not from day to day. Suppose that this demand is given in the form of specified total outflow rates from each origin headed towards each destination, for each origin-destination pair and for each time of day, and that some initial time-dependent routeinflow rates, meeting the given demand, are given. Finally, suppose that within-day time is represented by a continuous variable. This paper specifies a natural smooth day-to-day route-swapping procedure wherein drivers swap toward less expensive routes as day succeeds day, and shows that under reasonable conditions there is an equilibrium state of this dynamical system. If such a collection of route-inflows has arisen today, say, then there is no incentive for any route-inflow to change tomorrow, in the sense that at each moment of today each of today's route-inflows isalready on a route which today yielded the smallest travel cost. Such a set of “no-incentive-to-change” route-inflows is called adynamic equilibrium, or adynamic user-equilibrium, and may be regarded as a solution of the dynamic equilibrium traffic assignment problem. Thus, the paper introduces a smooth day-to-day dynamic assignment model and, using this model, shows that there is a dynamic user-equilibrium in a continuous time setting. The paper briefly considers the day-to-day stability of the route-swapping process, also in a continuous setting. Finally, the paper gives a simple dynamical example illustrating the stability of the route-swapping process in a simple two-route network when there is deterministic queueing at bottlenecks.

This paper studies reachability problems in discrete time affine systems on simplices-that is, how to steer the states in a simplex to a target polytope in finite time. Reachability problems in a discrete time setting have several distinct features from those in a continuous time setting and the solvability depends not only on the simplex itself but also on the target polytope. In this paper we first study the case where the union of the simplex and the target polytope is convex. Then we generalize the results by dropping the convex assumption. For theoretical completeness, the problem of making a polytope positive invariant is considered as well. Finally, a temperature control system is presented to illustrate our results.

Map labeling is a classical problem in cartography and geographic information systems (GIS) that asks to place labels for area, line, and point features, with the goal to select and place the maximum number of independent, i.e., overlap-free, labels. A practically interesting case is point labeling with axis-parallel rectangular labels of common size. In a fully dynamic setting, at each time step, either a new label appears or an existing label disappears. Then, the challenge is to maintain a maximum cardinality subset of pairwise independent labels with sub-linear update time. Motivated by this, we study the maximal independent set ((MIS)) and maximum independent set (Max-IS) problems on fully dynamic (insertion/deletion model) sets of axis-parallel rectangles of two types -- (i) uniform height and width and (ii) uniform height and arbitrary width; both settings can be modeled as rectangle intersection graphs. We present the first deterministic algorithm for maintaining an MIS (and thus a 4-approximate Max-IS) of a dynamic set of uniform rectangles with polylogarithmic update time. This breaks the natural barrier of $\Omega(\Delta)$ update time (where $\Delta$ is the maximum degree in the graph) for \emph{vertex updates} presented by Assadi et al. (STOC 2018). We continue by investigating Max-IS and provide a series of deterministic dynamic approximation schemes with approximation factors between 2 and 4 and corresponding running-time trade-offs. We have implemented our algorithms and reported the results of an experimental comparison exploring the trade-off between solution quality and update time for synthetic and real-world map labeling instances.

Support vector machines (SVM) have been extensively used for classification problems in many areas such as gene, text and image recognition. However, SVM have been rarely used to estimate the probability of default (PD) in credit risk. In this paper, we advocate the application of SVM, rather than the popular logistic regression (LR) method, for the estimation of both corporate and retail PD. Our results indicate that most of the time SVM outperforms LR in terms of classification accuracy for the corporate and retail segments. We propose a new wrapper feature selection based on maximizing the distance of the support vectors from the separating hyperplane and apply it to identify the main PD drivers. We used three datasets to test the PD estimation, containing (1) retail obligors from Germany, (2) corporate obligors from Eastern Europe, and (3) corporate obligors from Poland. Total assets, total liabilities, and sales are identified as frequent default drivers for the corporate datasets, whereas current account status and duration of the current account are frequent default drivers for the retail dataset.

Dynamic Parametric Portfolio Policy

This paper investigates the multifractal behavior of the probability of default (PD) of real sector firms and Turkey sovereign credit default swap (CDS). Moreover, we emphasize the co-movements of Hölder exponents during the financial crisis periods. For this reason, first, it is necessary to figure out the default probabilities of real sector firms. The default probability is evaluated weekly by the methodology of Moody’s Analytics, which is a commonly used approach, in which the market value of a firm is a call option written on its total assets. Multifractal detrended fluctuation analysis (MF-DFA), multifractal detrended cross-correlation analysis (MF-DCCA) and multifractal detrended moving average cross-correlation analysis (MF-X-DMA) techniques are applied to identify the multifractal behavior of the large-scale fluctuations of PDs and CDSs. In this way, we can evaluate the local Hurst exponents. Besides, the oscillation method is employed to estimate the pointwise and local Hölder exponents. In the period between January 2001 and March 2018, the structure of dynamic co-movements of Hölder exponents is determined by applying wavelet coherency methodology and the relations in crisis period are revealed. The selected period covers the crises with structural differences: Turkey banking crisis, the US sub-prime mortgage crisis and the European sovereign debt crisis that occurred in 2001, 2008 and 2009, respectively. Besides, during the periods of financial crises, among the local Hölder exponents, severely correlated large scales show multifractal features, and hence vector fractionally autoregressive integrated moving average (VFARIMA) forecasting provides better results than scalar models.

: To perform complex. interdependent, and urgent tasks in uncertain, unfamiliar, and often treacherous environments, the U.S. Army must be responsive, agile, versatile, and sustainable. These are the hallmarks of adaptive team performance -- the ability of team members to individually and cooperatively apply their knowledge and skills to the resolution of urgent, complex, novel, and ambiguous problems in dynamic work settings. Theory and research regarding the individual, team, and leader processes and characteristics that foster adaptive team performance are, unfortunately, quite limited. The authors conducted five interrelated research projects, combining research methods and approaches -- including comprehensive foundational literature reviews, theory development, experimental research in a laboratory setting, qualitative case study research, and longitudinal survey research in the field -- to build a new understanding of the ways in which leaders may enhance team learning, coordination, and adaptive performance in dynamic work environments.

We consider dynamic cooperative games in characteristic function form in the sense that the characteristic function evolves over time in accordance with a difference or differential equation that is influenced not only by the current ("instantaneous") characteristic function but also by the solution concept used to allocate the benefits of cooperation among the players. The latter solution concept can be any one of a number of now standard solution concepts of cooperative game theory but, for demonstration purposes, we focus on the core and the Shapley value. In the process, we introduce some new mechanisms by which players may regard the evolution of cooperative game over time and analyse them with respect to the goal of attaining time consistency either in discrete or in continuous time setting. In discrete time, we illustrate the phenomena that can arise when an allocation according to a given solution concept is used to adapt the values of coalitions at successive time points. In continuous time, we introduce the notion of an "instantaneous" game and its integration over time.

Tail generating functions for extendable branching processes

In a continuous time setting, we consider a set of -absolutely continuous probability measures, containing at least one equivalent to , and denote by , the smallest m-stable closed convex set of probability measures containing . We shall prove mainly under the martingale representation property with respect to a continuous vector valued martingale S, that is the set of supermartingale measures for a family , where is a set of predictable vector valued processes. We state as an immediate consequence of Föllmer-Kramkov Theorem in H. Föllmer and D. Kramkov (Optional decompositions under constraints, Probab. Theory Relat. Fields 109 (1997), pp. 1–25), the decomposition of -supermartingales.

We define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. Solutions exist and are unique under weaker assumptions than are needed in the continuous time setting. A comparison theorem for these solutions is also given. Applications to the theory of nonlinear expectations are explored, including a representation result.

We consider a discrete time hidden Markov model where the signal is a stationary Markov chain. When conditioned on the observations, the signal is a Markov chain in a random environment under the conditional measure. It is shown that this conditional signal is weakly ergodic when the signal is ergodic and the observations are nondegenerate. This permits a delicate exchange of the intersection and supremum of σ-fields, which is key for the stability of the nonlinear filter and partially resolves a long-standing gap in the proof of a result of Kunita [J. Multivariate Anal. 1 (1971) 365–393]. A similar result is obtained also in the continuous time setting. The proofs are based on an ergodic theorem for Markov chains in random environments in a general state space.

A minimum principle for chaotic dynamical systems

This note indicates two alternative proofs for a result of Galambos and Seneta [1] on the distribution of ratios of successive record times in a sequence of independent and identically distributed random variables. Some consequences of one method of proof are discussed, and its analogues in a continuous time setting are described.

Rotordynamics prediction in engineering (second edition)