Linear and nonlinear filtering in mathematical finance: a review

Copyright @ The Authors 2010This paper presents a review of time series filtering and its applications in mathematical finance. A summary of results of recent empirical studies with market data are presented for yield curve modelling and stochastic volatility modelling. The paper also outlines different approaches to filtering of nonlinear time series

An algorithm for moment-matching scenario generation with application to financial portfolio optimization

We present an algorithm for moment-matching scenario generation. This method produces scenarios and corresponding probability weights that match exactly the given mean, the covariance matrix, the average of the marginal skewness and the average of the marginal kurtosis of each individual component of a random vector. Optimisation is not employed in the scenario generation process and thus the method is computationally more advantageous than previous approaches. The algorithm is used for generating scenarios in a mean-CVaR portfolio optimisation model. For the chosen optimisation example, it is shown that desirable properties for a scenario generator are satisfied, including in-sample and out-of-sample stability. It is also shown that optimal solutions vary only marginally with increasing number of scenarios in this example; thus, good solutions can apparently be obtained with a relatively small number of scenarios. The proposed method can be used either on its own as a computationally inexpensive scenario generator or as a starting point for non-convex optimisation based scenario generators which aim to match all the third and the fourth order marginal moments (rather than average marginal moments)

Topological Interpretation of Barbero-Immirzi Parameter

We set up a canonical Hamiltonian formulation for a theory of gravity based on a Lagrangian density made up of the Hilbert-Palatini term and, instead of the Holst term, the Nieh-Yan topological density. The resulting set of constraints in the time gauge are shown to lead to a theory in terms of a real SU(2) connection which is exactly the same as that of Barbero and Immirzi with the coefficient of the Nieh-Yan term identified as the inverse of Barbero-Immirzi parameter. This provides a topological interpretation for this parameter. Matter coupling can then be introduced in the usual manner, {\em without} changing the universal topological Nieh-Yan term.Comment: 14 pages, revtex4, no figures. Minor modifications with additional remarks. References rearrange

A Construction of Solutions to Reflection Equations for Interaction-Round-a-Face Models

We present a procedure in which known solutions to reflection equations for interaction-round-a-face lattice models are used to construct new solutions. The procedure is particularly well-suited to models which have a known fusion hierarchy and which are based on graphs containing a node of valency $1$. Among such models are the Andrews-Baxter-Forrester models, for which we construct reflection equation solutions for fixed and free boundary conditions.Comment: 9 pages, LaTe

The Additional Symmetries for the BTL and CTL Hierarchies

The Toda lattice (TL) hierarchy was first introduced by K.Ueno and K.Takasaki in \cite{uenotaksasai} to generalize the Toda lattice equations\cite{toda}. Along the work of E. Date, M. Jimbo, M. Kashiwara and T. Miwa \cite{DJKM} on the KP hierarchy, K.Ueno and K.Takasaki in \cite{uenotaksasai} develop the theory for the TL hierarchy: its algebraic structure, the linearization, the bilinear identity, $\tau$ function and so on. Also the analogues of the B and C types for the TL hierarchy, i.e. the BTL and CTL hierarchies, are considered in \cite{uenotaksasai}, which are corresponding to infinite dimensional Lie algebras $\textmd{o}(\infty)$ and $\textmd{sp}(\infty)$ respectively. In this paper, we will focus on the study of the additional symmetries for the BTL and CTL hierarchies.Comment: 13 page

Fundamental Cycle of a Periodic Box-Ball System

We investigate a soliton cellular automaton (Box-Ball system) with periodic boundary conditions. Since the cellular automaton is a deterministic dynamical system that takes only a finite number of states, it will exhibit periodic motion. We determine its fundamental cycle for a given initial state.Comment: 28 pages, 6 figure

Integrable hierarchy underlying topological Landau-Ginzburg models of D-type

A universal integrable hierarchy underlying topological Landau-Ginzburg models of D-tye is presented. Like the dispersionless Toda hierarchy, the new hierarchy has two distinct (``positive" and ``negative") set of flows. Special solutions corresponding to topological Landau-Ginzburg models of D-type are characterized by a Riemann-Hilbert problem, which can be converted into a generalized hodograph transformation. This construction gives an embedding of the finite dimensional small phase space of these models into the full space of flows of this hierarchy. One of flat coordinates in the small phase space turns out to be identical to the first ``negative" time variable of the hierarchy, whereas the others belong to the ``positive" flows.Comment: 14 pages, Kyoto University KUCP-0061/9

Analysis of Strain Nonuniformity Index (SNI) in electrohydraulically formed sheet metal component

In sheet metal parts formed by Electrohydraulic (free forming) process, a spherically shaped reflector is predicted to result in a highly non-uniform thickness strain distribution. As expected, the thickness strain (and hence thinning) is maximum at the top of the formed dome. The probability of failure is therefore highest at this location. A finite element model is formulated in ABAQUS explicit to generate the strain distribution in sheet metal. The model considers a water filled chamber to transmit the pressure pulse. The effect of the electrical discharge between the electrodes is modeled as a pressure wave of a certain magnitude originating from the location of the electrodes. The constitutive relation for the sheet is described by the Johnson-Cook model and non-deformable/ stiff tools are used. The extent of non-uniformity in thickness strain distribution has been expressed in terms of Strain Non-uniformity Index (SNI). It is the difference between the peak thickness strain (PTS) and the average thickness strain (ATS). For successful forming, the value of SNI should be as low as possible. This is enabled by an alternate design of the reflector which is compared with the spherical shape. The pros and cons of using either shape of reflector are examined in the paper

The Multicomponent KP Hierarchy: Differential Fay Identities and Lax Equations

In this article, we show that four sets of differential Fay identities of an $N$-component KP hierarchy derived from the bilinear relation satisfied by the tau function of the hierarchy are sufficient to derive the auxiliary linear equations for the wave functions. From this, we derive the Lax representation for the $N$-component KP hierarchy, which are equations satisfied by some pseudodifferential operators with matrix coefficients. Besides the Lax equations with respect to the time variables proposed in \cite{2}, we also obtain a set of equations relating different charge sectors, which can be considered as a generalization of the modified KP hierarchy proposed in \cite{3}.Comment: 19 page

Tissue factor-bearing microparticles and inflammation: a potential mechanism for the development of venous thromboembolism in cancer

© 2017 International Society on Thrombosis and Haemostasis Summary: Cancer is associated with an increased risk of venous thromboembolism (VTE); the exact mechanisms for the induction of VTE remain to be fully elucidated, but it is widely acknowledged that tissue factor (TF)-bearing microparticles (TF-MPs) may play a significant role. However, TF-MPs have yet to be accepted as a genuine biomarker for cancer-associated VTE, as the presence of elevated TF-MP levels is not always accompanied by thrombosis; interestingly, in certain cases, particularly in pancreatic cancer, VTE seems to be more likely in the context of acute inflammation. Although several potential mechanisms for the development of VTE in cancer have been postulated, this review explores the homeostatic disruption of TF-MPs, as the main reservoir of bloodborne TF, in the context of cancer and inflammation, and considers the abrogated responses of the activated endothelium and mononuclear phagocyte system in mediating this disruption