Reliability properties under a stopping time shift

Considering a series representation of a coherent system using a shift transform of the components lifetime T-i, at its critical level Y-i, we study two problems. First, under such a shift transform, we analyse the preservation properties of the non-parametric distribution classes and secondly the association preserving property of the components lifetime under such transformations. (c) 2007 Elsevier B.V. All rights reserved.

Linear quadratic Gaussian control of discrete-time Markov jump linear systems with horizon defined by stopping times

The linear quadratic Gaussian control of discrete-time Markov jump linear systems is addressed in this paper, first for state feedback, and also for dynamic output feedback using state estimation. in the model studied, the problem horizon is defined by a stopping time τ which represents either, the occurrence of a fix number N of failures or repairs (T N), or the occurrence of a crucial failure event (τ δ), after which the system paralyzed. From the constructive method used here a separation principle holds, and the solutions are given in terms of a Kalman filter and a state feedback sequence of controls. The control gains are obtained by recursions from a set of algebraic Riccati equations for the former case or by a coupled set of algebraic Riccati equation for the latter case. Copyright © 2005 IFAC.

The LQ control problem for Markovian jumps linear systems with horizon defined by stopping times

This paper deals with a stochastic optimal control problem involving discrete-time jump Markov linear systems. The jumps or changes between the system operation modes evolve according to an underlying Markov chain. In the model studied, the problem horizon is defined by a stopping time τ which represents either, the occurrence of a fix number N of failures or repairs (TN), or the occurrence of a crucial failure event (τΔ), after which the system is brought to a halt for maintenance. In addition, an intermediary mixed case for which T represents the minimum between TN and τΔ is also considered. These stopping times coincide with some of the jump times of the Markov state and the information available allows the reconfiguration of the control action at each jump time, in the form of a linear feedback gain. The solution for the linear quadratic problem with complete Markov state observation is presented. The solution is given in terms of recursions of a set of algebraic Riccati equations (ARE) or a coupled set of algebraic Riccati equation (CARE).

Asymptotic Change-Point Analysis of the Dependencies in Time Series

In recent papers, Wied and his coauthors have introduced change-point procedures to detect and estimate structural breaks in the correlation between time series. To prove the asymptotic distribution of the test statistic and stopping time as well as the change-point estimation rate, they use an extended functional Delta method and assume nearly constant expectations and variances of the time series. In this thesis, we allow asymptotically infinitely many structural breaks in the means and variances of the time series. For this setting, we present test statistics and stopping times which are used to determine whether or not the correlation between two time series is and stays constant, respectively. Additionally, we consider estimates for change-points in the correlations. The employed nonparametric statistics depend on the means and variances. These (nuisance) parameters are replaced by estimates in the course of this thesis. We avoid assuming a fixed form of these estimates but rather we use "blackbox" estimates, i.e. we derive results under assumptions that these estimates fulfill. These results are supplement with examples. This thesis is organized in seven sections. In Section 1, we motivate the issue and present the mathematical model. In Section 2, we consider a posteriori and sequential testing procedures, and investigate convergence rates for change-point estimation, always assuming that the means and the variances of the time series are known. In the following sections, the assumptions of known means and variances are relaxed. In Section 3, we present the assumptions for the mean and variance estimates that we will use for the mean in Section 4, for the variance in Section 5, and for both parameters in Section 6. Finally, in Section 7, a simulation study illustrates the finite sample behaviors of some testing procedures and estimates.

Valuing American Derivatives by Least Squares Methods

Least Squares estimators are notoriously known to generate sub-optimal exercise decisions when determining the optimal stopping time. The consequence is that the price of the option is underestimated. We show how variance reduction methods can be implemented to obtain more accurate option prices. We also extend the Longsta¤ and Schwartz (2001) method to price American options under stochastic volatility. These are two important contributions that are particularly relevant for practitioners. Finally, we extend the Glasserman and Yu (2004b) methodology to price Asian options and basket options.

Anaerobic performance in ice hockey : the effect of skate blade radius of hollow

The purpose of the study was to investigate the effect of skate blade radius of hollow (ROH) on anaerobic performance, specifically during the acceleration and stopping phases of an on-ice skating test. Fifteen, male Junior B hockey players (mean age 19 y ± 1.46) were recruited to participate. On-icc testing required each participant to complete an on-ice anaerobic performance test [Reed Repeat Skate (RRS)) on three separate days. During each on-ice test, the participant's skate blades were sharpened to one of three, randomly assigned, ROH values (0.63 cm, 1.27 cm, 1.90 cm). Performance times were recorded during each RRS and used to calculate anaerobic variables [anaerobic power (W), anaerobic capacity (W), and fatigue index (s, %)). Each RRS was video recorded for the purpose of motion analysis. Video footage was imported into Peak Motus™ to measure kinematic variables of the acceleration and stopping phases. The specific variables calculated from the acceleration phase were: average velocity over 6 m (m/s), average stride length (m), and mean stride rate (strides/s). The specific variables calculated from the stopping phase were: velocity at initiation of stopping (rn/s), stopping distance (m), stopping time (s). A repeated measures ANOV A was used to assess differences in mean performance and kinematic variables across the three selected hollows. Further analysis was conducted to assess differences in trial by trial performance and kinematic variables for all hollows. The primary findings of the study suggested that skate blade ROH can have a significant effect on kinematic variables, namely stride length and stride rate during the acceleration phase and stopping distance and stopping time during the stopping phase of an on-ice anaerobic performance test. During the acceleration phase, no significant difdifferences were found in SR and SL across the three selected hollows. Mean SR on the 1.27 cm hollow was significantly slower than both the 0.63 cm and 1.90 cm hollows and SL was significantly longer when skating on the 1.27 cm hollow in comparison to the 1.90 cm hollow. During the stopping phase, stopping distance on the 0.63 cm hollow (4.12 m ± 0.14) was significantly shorter than both the 1.27 cm hollow (4.43 m ± 0.08) (p < 0.05) and the 1.90 cm ho])ow (4.35 m ± 0.12) (p < 0.05). Mean ST was also significantly shorter when stopping on the 0.63 cm hollow then both the 1.27 cm and 1.90 cm hollows. Trial by trial results clearly illustrated the affect of fatigue on kinematic variables; AV, SR, IV decreased from trial 1 to 6. There was no significant effect on anaerobic performance variables during the RRS. Altering the skate blade ROH has a significant and practical affect on accelerating and stopping performance will be discussed in this paper.

Ensaios em Finanças

Esta tese é composta de três artigos sobre finanças. O primeiro tem o título "Nonparametric Option Pricing with Generalized Entropic Estimators " e estuda um método de apreçamento de derivativos em mercados incompletos. Este método está relacionado com membros da família de funções de Cressie-Read em que cada membro fornece uma medida neutra ao risco. Vários testes são feitos. Os resultados destes testes sugerem um modo de definir um intervalo robusto para preços de opções. Os outros dois artigos são sobre anúncios agendados em diferentes situações. O segundo se chama "Watching the News: Optimal Stopping Time and Scheduled Announcements" e estuda problemas de tempo de parada ótimo na presença de saltos numa data fixa em modelos de difusão com salto. Fornece resultados sobre a otimalidade do tempo de parada um pouco antes do anúncio. O artigo aplica os resultados ao tempo de exercício de Opções Americanas e ao tempo ótimo de venda de um ativo. Finalmente o terceiro artigo estuda um problema de carteira ótima na presença de custo fixo quando os preços podem saltar numa data fixa. Seu título é "Dynamic Portfolio Selection with Transactions Costs and Scheduled Announcement" e o resultado mais interessante é que o comportamento do investidor é consistente com estudos empíricos sobre volume de transações em momentos próximos de anúncios.

Stochastic Stability for Markovian Jump Linear Systems Subject to a Crucial Failure Event

This paper is concerned with the stability of discrete-time linear systems subject to random jumps in the parameters, described by an underlying finite-state Markov chain. In the model studied, a stopping time τ Δ is associated with the occurrence of a crucial failure after which the system is brought to a halt for maintenance. The usual stochastic stability concepts and associated results are not indicated, since they are tailored to pure infinite horizon problems. Using the concept named stochastic τ-stability, equivalent conditions to ensure the stochastic stability of the system until the occurrence of τ Δ is obtained. In addition, an intermediary and mixed case for which τ represents the minimum between the occurrence of a fix number N of failures and the occurrence of a crucial failure τ Δ is also considered. Necessary and sufficient conditions to ensure the stochastic τ-stability are provided in this setting that are auxiliary to the main result.

Estabilidade estocástica de sistemas lineares com Saltos Markovianos e Sistemas Lineares com Saltos Semimarkovianos

Pós-graduação em Matematica Aplicada e Computacional - FCT

Tempo, finitude, velhice e fotografia

This article analyzes and discusses the experience of time in old age through the relations of the elderly with photography. We did photography workshops with a group of elders exploring with them the sense of the photographic act death, as an act of freezing and stopping time and also the sense of exploring the future to create, through the photographic act, an image that can symbolize moving on in life.

Optimal eradication: when to stop looking for an invasive plant

The notion of being sure that you have completely eradicated an invasive species is fanciful because of imperfect detection and persistent seed banks. Eradication is commonly declared either on an ad hoc basis, on notions of seed bank longevity, or on setting arbitrary thresholds of 1% or 5% confidence that the species is not present. Rather than declaring eradication at some arbitrary level of confidence, we take an economic approach in which we stop looking when the expected costs outweigh the expected benefits. We develop theory that determines the number of years of absent surveys required to minimize the net expected cost. Given detection of a species is imperfect, the optimal stopping time is a trade-off between the cost of continued surveying and the cost of escape and damage if eradication is declared too soon. A simple rule of thumb compares well to the exact optimal solution using stochastic dynamic programming. Application of the approach to the eradication programme of Helenium amarum reveals that the actual stopping time was a precautionary one given the ranges for each parameter.

A Unified Model for XVA, including Interest Rates and Rating

We start in Chapter 2 to investigate linear matrix-valued SDEs and the Itô-stochastic Magnus expansion. The Itô-stochastic Magnus expansion provides an efficient numerical scheme to solve matrix-valued SDEs. We show convergence of the expansion up to a stopping time τ and provide an asymptotic estimate of the cumulative distribution function of τ. Moreover, we show how to apply it to solve SPDEs with one and two spatial dimensions by combining it with the method of lines with high accuracy. We will see that the Magnus expansion allows us to use GPU techniques leading to major performance improvements compared to a standard Euler-Maruyama scheme. In Chapter 3, we study a short-rate model in a Cox-Ingersoll-Ross (CIR) framework for negative interest rates. We define the short rate as the difference of two independent CIR processes and add a deterministic shift to guarantee a perfect fit to the market term structure. We show how to use the Gram-Charlier expansion to efficiently calibrate the model to the market swaption surface and price Bermudan swaptions with good accuracy. We are taking two different perspectives for rating transition modelling. In Section 4.4, we study inhomogeneous continuous-time Markov chains (ICTMC) as a candidate for a rating model with deterministic rating transitions. We extend this model by taking a Lie group perspective in Section 4.5, to allow for stochastic rating transitions. In both cases, we will compare the most popular choices for a change of measure technique and show how to efficiently calibrate both models to the available historical rating data and market default probabilities. At the very end, we apply the techniques shown in this thesis to minimize the collateral-inclusive Credit/ Debit Valuation Adjustments under the constraint of small collateral postings by using a collateral account dependent on rating trigger.

Intracranial EEG reveals a time- and frequency-specific role for the right inferior frontal gyrus and primary motor cortex in stopping initiated responses.

Inappropriate response tendencies may be stopped via a specific fronto/basal ganglia/primary motor cortical network. We sought to characterize the functional role of two regions in this putative stopping network, the right inferior frontal gyrus (IFG) and the primary motor cortex (M1), using electocorticography from subdural electrodes in four patients while they performed a stop-signal task. On each trial, a motor response was initiated, and on a minority of trials a stop signal instructed the patient to try to stop the response. For each patient, there was a greater right IFG response in the beta frequency band ( approximately 16 Hz) for successful versus unsuccessful stop trials. This finding adds to evidence for a functional network for stopping because changes in beta frequency activity have also been observed in the basal ganglia in association with behavioral stopping. In addition, the right IFG response occurred 100-250 ms after the stop signal, a time range consistent with a putative inhibitory control process rather than with stop-signal processing or feedback regarding success. A downstream target of inhibitory control is M1. In each patient, there was alpha/beta band desynchronization in M1 for stop trials. However, the degree of desynchronization in M1 was less for successfully than unsuccessfully stopped trials. This reduced desynchronization on successful stop trials could relate to increased GABA inhibition in M1. Together with other findings, the results suggest that behavioral stopping is implemented via synchronized activity in the beta frequency band in a right IFG/basal ganglia network, with downstream effects on M1.

Implementation of a unified userspace time handling library under the Linux OS

An appropriate assessment of end-to-end network performance presumes highly efficient time tracking and measurement with precise time control of the stopping and resuming of program operation. In this paper, a novel approach to solving the problems of highly efficient and precise time measurements on PC-platforms and on ARM-architectures is proposed. A new unified High Performance Timer and a corresponding software library offer a unified interface to the known time counters and automatically identify the fastest and most reliable time source, available in the user space of a computing system. The research is focused on developing an approach of unified time acquisition from the PC hardware and accordingly substituting the common way of getting the time value through Linux system calls. The presented approach provides a much faster means of obtaining the time values with a nanosecond precision than by using conventional means. Moreover, it is capable of handling the sequential time value, precise sleep functions and process resuming. This ability means the reduction of wasting computer resources during the execution of a sleeping process from 100% (busy-wait) to 1-1.5%, whereas the benefits of very accurate process resuming times on long waits are maintained.

Geometric stopping of a random walk and its applications to valuing equity-linked death benefits

We study discrete-time models in which death benefits can depend on a stock price index, the logarithm of which is modeled as a random walk. Examples of such benefit payments include put and call options, barrier options, and lookback options. Because the distribution of the curtate-future-lifetime can be approximated by a linear combination of geometric distributions, it suffices to consider curtate-future-lifetimes with a geometric distribution. In binomial and trinomial tree models, closed-form expressions for the expectations of the discounted benefit payment are obtained for a series of options. They are based on results concerning geometric stopping of a random walk, in particular also on a version of the Wiener-Hopf factorization.