EXPLICIT STRONG SOLUTIONS OF MULTIDIMENSIONAL STOCHASTIC DIFFERENTIAL EQUATIONS

Herein, we characterize strong solutions of multidimensional stochastic differential equations (formula) that can be represented locally as (formula) where W is an multidimensional Brownian motion and U, (symbole) are continuous functions. Assuming that (symbole) is continuously differentiable, we find that (symbole) must satisfy a commutation relation for such explicit solutions to exist and we identify all drift terms b as well as U and (symbole) that will allow X to be represented in this manner. Our method is based on the existence of a local change of coordinates in terms of a diffeomorphism between the solutions X and the strong solutions to a simpler Ito integral equation.Diffeomorphism, Ito processes, explicit solutions.

Option pricing and hedging for regime-switching geometric Brownian motion models

We find the variance-optimal equivalent martingale measure when multivariate assets are modeled by a regime-switching geometric Brownian motion, and the regimes are represented by a homogeneous continuous time Markov chain. Under this new measure, the Markov chain driving the regimes is no longer homogeneous, which differs from the equivalent martingale measures usually proposed in the literature. We show the solution minimizes the mean-variance hedging error under the objective measure. As argued by \citet{Schweizer:1996}, the variance-optimal equivalent measure naturally extends canonical option pricing results to the case of an incomplete market and the expectation under the proposed measure may be interpreted as an option price. Solutions for the option value and the optimal hedging strategy are easily obtained from Monte Carlo simulations. Two applications are considered

Central limit theorems for martingales-II: convergence in the weak dual topology

A convergence theorem for martingales with c\`adl\`ag trajectories (right continuous with left limits everywhere) is obtained in the sense of the weak dual topology on Hilbert space, under conditions that are much weaker than those required for any of the usual Skorohod topologies. Examples are provided to show that these conditions are also very easy to check and yield useful asymptotic results, especially when the limit is a mixture of stochastic processes with discontinuities

Tests of independence and randomness for arbitrary data using copula-based covariances

In this article, we study tests of independence for data with arbitrary distributions in the non-serial case, i.e., for independent and identically distributed random vectors, as well as in the serial case, i.e., for time series. These tests are derived from copula-based covariances and their multivariate extensions using M\"obius transforms. We find the asymptotic distributions of the statistics under the null hypothesis of independence or randomness, as well as under contiguous alternatives. This enables us to find out locally most powerful test statistics for some alternatives, whatever the margins. Numerical experiments are performed for Wald's type combinations of these statistics to assess the finite sample performance

Multivariate General Compound Point Processes in Limit Order Books

In this paper, we focus on a new generalization of multivariate general compound Hawkes process (MGCHP), which we referred to as the multivariate general compound point process (MGCPP). Namely, we applied a multivariate point process to model the order flow instead of the Hawkes process. Law of large numbers (LLN) and two functional central limit theorems (FCLTs) for the MGCPP were proved in this work. Applications of the MGCPP in the limit order market were also considered. We provided numerical simulations and comparisons for the MGCPP and MGCHP by applying Google, Apple, Microsoft, Amazon, and Intel trading data.Comment: 16 pages and 14 figure

On factor copula-based mixed regression models

In this article, a copula-based method for mixed regression models is proposed, where the conditional distribution of the response variable, given covariates, is modelled by a parametric family of continuous or discrete distributions, and the effect of a common latent variable pertaining to a cluster is modelled with a factor copula. We show how to estimate the parameters of the copula and the parameters of the margins, and we find the asymptotic behaviour of the estimation errors. Numerical experiments are performed to assess the precision of the estimators for finite samples. An example of an application is given using COVID-19 vaccination hesitancy from several countries. Computations are based on R package CopulaGAMM

Di-μ-bromido-bis­{[N,N-dimethyl-N′-(thio­phen-2-yl­methyl­idene)ethane-1,2-diamine]­copper(I)]}

In the crystal structure of the title compound, [Cu2Br2(C9H14N2S)2], the mol­ecule resides about a crystallographic inversion center. The coordination sphere around each copper ion has a distorted tetra­hedral geometry, with ligation by two bridging bromide ions, an amine N atom and an imine N atom. The thio­phene ring is disordered over two sites, with occupancies of 0.719 (3) and 0.281 (3). Weak C—H⋯π inter­actions feature in the crystal packing

The risk of stroke recurrence in patients with atrial fibrillation and reduced ejection fraction

Abstract Background: Atrial fibrillation (AF) and congestive heart failure often coexist due to their shared risk factors leading to potential worse outcome, particularly cerebrovascular events. The aims of this study were to calculate the rates of ischemic and severe bleeding events in ischemic stroke patients having both AF and reduced ejection fraction (rEF) (⩽40%), compared to ischemic stroke patients with AF but without rEF. Methods: We performed a retrospective analysis that drew data from prospective studies. The primary outcome was the composite of either ischemic (stroke or systemic embolism), or hemorrhagic events (symptomatic intracranial bleeding and severe extracranial bleeding). Results: The cohort for this analysis comprised 3477 patients with ischemic stroke and AF, of which, 643 (18.3%) had also rEF. After a mean follow-up of 7.5 ± 9.1 months, 375 (10.8%) patients had 382 recorded outcome events, for an annual rate of 18.0%. While the number of primary outcome events in patients with rEF was 86 (13.4%), compared to 289 (10.2%) for the patients without rEF; on multivariable analysis rEF was not associated with the primary outcome (OR 1.25; 95% CI 0.84–1.88). At the end of follow-up, 321 (49.9%) patients with rEF were deceased or disabled (mRS ⩾3), compared with 1145 (40.4%) of those without rEF; on multivariable analysis, rEF was correlated with mortality or disability (OR 1.35; 95% CI 1.03–1.77). Conclusions: In patients with ischemic stroke and AF, the presence of rEF was not associated with the composite outcome of ischemic or hemorrhagic events over short-term follow-up but was associated with increased mortality or disability