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.

Exit times in non-Markovian drifting continuous-time random-walk processes

By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show that when drift and jumps have the same sign the relevant integral equations can be solved in closed form. The case when holding times have the classical Erlang distribution is considered in detail.

Persistent random walk model for transport trough thin slabs

We present a model for transport in multiply scattering media based on a three-dimensional generalization of the persistent random walk. The model assumes that photons move along directions that are parallel to the axes. Although this hypothesis is not realistic, it allows us to solve exactly the problem of multiple scattering propagation in a thin slab. Among other quantities, the transmission probability and the mean transmission time can be calculated exactly. Besides being completely solvable, the model could be used as a benchmark for approximation schemes to multiple light scattering.

Random walk radiosity with generalized absorption probabilities

The author studies random walk estimators for radiosity with generalized absorption probabilities. That is, a path will either die or survive on a patch according to an arbitrary probability. The estimators studied so far, the infinite path length estimator and finite path length one, can be considered as particular cases. Practical applications of the random walks with generalized probabilities are given. A necessary and sufficient condition for the existence of the variance is given, together with heuristics to be used in practical cases. The optimal probabilities are also found for the case when one is interested in the whole scene, and are equal to the reflectivities

Testing the Random Walk Hypothesis on the Baltic Stock Markets

The purpose of the thesis is to analyze whether the returns of general stock market indices of Estonia, Latvia and Lithuania follow the random walk hypothesis (RWH), and in addition, whether they are consistent with the weak-form efficiency criterion. Also the existence of the day-of-the-week anomaly is examined in the same regional markets. The data consists of daily closing quotes of the OMX Tallinn, Riga and Vilnius total return indices for the sample period from January 3, 2000 to August 28, 2009. Moreover, the full sample period is also divided into two sub-periods. The RWH is tested by applying three quantitative methods (i.e. the Augmented Dickey-Fuller unit root test, serial correlation test and non-parametric runs test). Ordinary Least Squares (OLS) regression with dummy variables is employed to detect the day-of-the-week anomalies. The random walk hypothesis (RWH) is rejected in the Estonian and Lithuanian stock markets. The Latvian stock market exhibits more efficient behaviour, although some evidence of inefficiency is also found, mostly during the first sub-period from 2000 to 2004. Day-of-the-week anomalies are detected on every stock market examined, though no longer during the later sub-period.

Passeig per l’invisible: itinerari químic per la ciutat de Girona = A walk through the invisible: a chemical journey through Girona

The presented itinerary covers eleven sites of the city of Girona that have been chosen for their interest from a chemical point of view. Girona is a city with chemistry, and this journey allowed student to see that chemistry is present everywhere, even in everyday life and not only in classrooms and laboratories. This approach aims to motivate students to discover something that had been invisible

The six-minute walk test and body weight-walk distance product in healthy Brazilian subjects

We assessed the 6-min walk distance (6MWD) and body weight x distance product (6MWw) in healthy Brazilian subjects and compared measured 6MWD with values predicted in five reference equations developed for other populations. Anthropometry, spirometry, reported physical activity, and two walk tests in a 30-m corridor were evaluated in 134 subjects (73 females, 13-84 years). Mean 6MWD and 6MWw were significantly greater in males than in females (622 ± 80 m, 46,322 ± 10,539 kg.m vs 551 ± 71 m, 36,356 ± 8,289 kg.m, P < 0.05). Four equations significantly overestimated measured 6MWD (range, 32 ± 71 to 137 ± 74 m; P < 0.001), and one significantly underestimated it (-36 ± 86 m; P < 0.001). 6MWD significantly correlated with age (r = -0.39), height (r = 0.44), body mass index (r = -0.24), and reported physical activity (r = 0.25). 6MWw significantly correlated with age (r = -0.21), height (r = 0.66) and reported physical activity (r = 0.25). The reference equation devised for walk distance was 6MWDm = 622.461 - (1.846 x Ageyears) + (61.503 x Gendermales = 1; females = 0); r2 = 0.300. In an additional group of 85 subjects prospectively studied, the difference between measured and the 6MWD predicted with the equation proposed here was not significant (-3 ± 68 m; P = 0.938). The measured 6MWD represented 99.6 ± 11.9% of the predicted value. We conclude that 6MWD and 6MWw variances were adequately explained by demographic and anthropometric attributes. This reference equation is probably most appropriate for evaluating the exercise capacity of Brazilian patients with chronic diseases.

Reliability and validity of heart rate variability threshold assessment during an incremental shuttle-walk test in middle-aged and older adults

Studies on the assessment of heart rate variability threshold (HRVT) during walking are scarce. We determined the reliability and validity of HRVT assessment during the incremental shuttle walk test (ISWT) in healthy subjects. Thirty-one participants aged 57 ± 9 years (17 females) performed 3 ISWTs. During the 1st and 2nd ISWTs, instantaneous heart rate variability was calculated every 30 s and HRVT was measured. Walking velocity at HRVT in these tests (WV-HRVT1 and WV-HRVT2) was registered. During the 3rd ISWT, physiological responses were assessed. The ventilatory equivalents were used to determine ventilatory threshold (VT) and the WV at VT (WV-VT) was recorded. The difference between WV-HRVT1 and WV-HRVT2 was not statistically significant (median and interquartile range = 4.8; 4.8 to 5.4 vs4.8; 4.2 to 5.4 km/h); the correlation between WV-HRVT1 and WV-HRVT2 was significant (r = 0.84); the intraclass correlation coefficient was high (0.92; 0.82 to 0.96), and the agreement was acceptable (-0.08 km/h; -0.92 to 0.87). The difference between WV-VT and WV-HRVT2 was not statistically significant (4.8; 4.8 to 5.4 vs 4.8; 4.2 to 5.4 km/h) and the agreement was acceptable (0.04 km/h; -1.28 to 1.36). HRVT assessment during walking is a reliable measure and permits the estimation of VT in adults. We suggest the use of the ISWT for the assessment of exercise capacity in middle-aged and older adults.

Intensity and physiological responses to the 6-minute walk test in middle-aged and older adults: a comparison with cardiopulmonary exercise testing

The 6-minute walk test (6MWT) is a simple field test that is widely used in clinical settings to assess functional exercise capacity. However, studies with healthy subjects are scarce. We hypothesized that the 6MWT might be useful to assess exercise capacity in healthy subjects. The purpose of this study was to evaluate 6MWT intensity in middle-aged and older adults, as well as to develop a simple equation to predict oxygen uptake ( V ˙ O 2 ) from the 6-min walk distance (6MWD). Eighty-six participants, 40 men and 46 women, 40-74 years of age and with a mean body mass index of 28±6 kg/m2, performed the 6MWT according to American Thoracic Society guidelines. Physiological responses were evaluated during the 6MWT using a K4b2 Cosmed telemetry gas analyzer. On a different occasion, the subjects performed ramp protocol cardiopulmonary exercise testing (CPET) on a treadmill. Peak V ˙ O 2 in the 6MWT corresponded to 78±13% of the peak V ˙ O 2 during CPET, and the maximum heart rate corresponded to 80±23% of that obtained in CPET. Peak V ˙ O 2 in CPET was adequately predicted by the 6MWD by a linear regression equation: V ˙ O 2 mL·min-1·kg-1 = -2.863 + (0.0563×6MWDm) (R2=0.76). The 6MWT represents a moderate-to-high intensity activity in middle-aged and older adults and proved to be useful for predicting cardiorespiratory fitness in the present study. Our results suggest that the 6MWT may also be useful in asymptomatic individuals, and its use in walk-based conditioning programs should be encouraged.

I must walk through the gate : an ontological necessity

This research is a self-study into my life as an athlete, elementary school teacher, leamer, and as a teacher educator/academic. Throughout the inquiry, I explore how my beliefs and values infused my lived experiences and ultimately influenced my constructivist, humanist, and ultimately my holistic teaching and learning practice which at times disrupted the status quo. I have written a collection of narratives (data generation) which embodied my identity as an unintelligent student/leamer, a teacher/learner, an experiential learner, a tenacious participant, and a change agent to name a few. As I unpack my stories and hermeneutically reconstruct their intent, I question their meaning as I explore how I can improve my teaching and learning practice and potentially effect positive change when instructing beginning teacher candidates at a Faculty of Education. At the outset I situate my story and provide the necessary political, social, and cultural background information to ground my research. I follow this with an in depth look at the elements that interconnect the theoretical framework of this self-study by presenting the notion of writing at the boundaries through auto ethnography (Ellis, 2000; Ellis & Bochner, 2004) and writing as a method of inquiry (Richardson, 2000). The emergent themes of experiential learning, identity, and embodied knowing surfaced during the data generation phase. I use the Probyn' s (1990) .. metaphor of locatedness to unpack these themes and ponder the question, Where is experience located? I deepen the exploration by layering Drake's (2007) KnowlDo/Be framework alongside locatedness and offer descriptions of learning moments grounded in pedagogical theories. In the final phase, I introduce thirdspace theory (Bhabha, 1994; Soja, 1996) as a space that allowed me to puzzle educational dilemmas and begin to reconcile the binaries that existed in my life both personally, and professionally. I end where I began by revisiting the questions that drove this study. In addition, Ireflect upon the writing process and the challenges that I encountered while immersed in this approach and contemplate the relevance of conducting a self-study. I leave the reader with what is waiting for me on the other side of the gate, for as Henry James suggested, "Experience is never limited, and it is never complete."