Brownian excursions outside a corridor and two-sided Parisian options

In this paper, we study the excursion time of a Brownian motion with drift outside a corridor by using a four states semi-Markov model. In mathematical finance, these results have an important application in the valuation of double barrier Parisian options. In this paper, we obtain an explicit expression for the Laplace transform of its price

A dynamic contagion process and an application to credit risk

We introduce a new point process, the dynamic contagion process, by gener- alising the Hawkes process and the Cox process with shot noise intensity. Our process includes both self-excited and externally excited jumps, which could be used to model the dynamic contagion impact from endogenous and exoge- nous factors of the underlying system. We have systematically analysed the theoretical distributional properties of this new process, based on the piece- wise deterministic Markov process theory developed by Davis (1984), and the extension of the martingale methodology used by Dassios and Jang (2003). The analytic expressions of the Laplace transform of the intensity process and the probability generating function of the point process have been de- rived. An explicit example of specified jumps with exponential distributions is also given. The object of this study is to produce a general mathemati- cal framework for modelling the dependence structure of arriving events with dynamic contagion, which has the potential to be applicable to a variety of problems in economics, finance and insurance. We provide an application of this process to credit risk, and the simulation algorithm for further industrial implementation and statistical analysis

Exact simulation of Poisson-Dirichlet distribution and generalised gamma process

Let J1> J2> ⋯ be the ranked jumps of a gamma process τα on the time interval [0 , α] , such that τα=∑k=1∞Jk . In this paper, we design an algorithm that samples from the random vector (J1,⋯,JN,∑k=N+1∞Jk) . Our algorithm provides an analog to the well-established inverse Lévy measure (ILM) algorithm by replacing the numerical inversion of exponential integral with an acceptance-rejection step. This research is motivated by the construction of Dirichlet process prior in Bayesian nonparametric statistics. The prior assigns weight to each atom according to a GEM distribution, and the simulation algorithm enables us to sample from the N largest random weights of the prior. Then we extend the simulation algorithm to a generalised gamma process. The simulation problem of inhomogeneous processes will also be considered. Numerical implementations are provided to illustrate the effectiveness of our algorithms

Wave scattering by small impedance particles in a medium

The theory of acoustic wave scattering by many small bodies is developed for bodies with impedance boundary condition. It is shown that if one embeds many small particles in a bounded domain, filled with a known material, then one can create a new material with the properties very different from the properties of the original material. Moreover, these very different properties occur although the total volume of the embedded small particles is negligible compared with the volume of the original material

Determinants of inspiratory muscle function in healthy children

AbstractBackgroundChildren are affected by disorders that have an impact on the respiratory muscles. Inspiratory muscle function can be assessed by means of the noninvasive tension–time index of the inspiratory muscles (TTImus). Our objectives were to identify the determinants of TTImus in healthy children and to report normal values of TTImus in this population.MethodsWe measured weight, height, upper arm muscle area (UAMA), and TTImus in 96 children aged 6–18 years. The level and frequency of aerobic activity was assessed by questionnaire.ResultsTTImus was significantly lower in male subjects (0.095 ± 0.038, mean ± SD) compared with female subjects (0.126 ± 0.056) (p = 0.002). TTImus was significantly lower in regularly exercising (0.093 ± 0.040) compared with nonexercising subjects (0.130 ± 0.053) (p < 0.001). TTImus was significantly negatively related to age (r = −0.239, p = 0.019), weight (r = −0.214, p = 0.037), height (r = −0.355, p < 0.001), and UAMA (r = −0.222, p = 0.030). Multivariate logistic regression analysis revealed that height and aerobic exercise were significantly related to TTImus independently of age, weight, and UAMA. The predictive regression equation for TTImus in male subjects was TTImus = 0.228 − 0.001 × height (cm), and in female subjects it was TTImus = 0.320 − 0.001 × height (cm) .ConclusionGender, age, anthropometry, skeletal muscularity, and aerobic exercise are significantly associated with indices of inspiratory muscle function in children. Normal values of TTImus in healthy children are reported