A Diffusion Approximation to the Markov Chains Model of the Financial Market and the Expected Riskless Profit Under Selling of Call and Put Options

A discrete time model of financial markets is considered. It is assumed that the stock price evolution is described by a homogeneous Markov chain. In the focus of attention is the expected value of the guaranteed profit of the investor that arises when the jumps of the stock price are bounded. The suggested diffusion approximation for the Markov chain allows establishing a convenient approximate formula for the studied characteristic.Ergodic and irreducible Markov chains, Stationary distribution, Local limit theorem, Upper hedge, Upper rational price

A Diffusion Approximation for the Riskless Profit Under Selling of Discrete Time Call Options. Non-identically Distributed Jumps

A discrete time model of financial markets is considered. It is assumed that the relative jumps of the risky security price are independent non-identically distributed random variables. In the focus of attention is the expected non-risky profit of the investor that arises when the jumps of the stock price are bounded while the investor follows the upper hedge. The considered discrete time model is approximated by a continuous time model that generalizes the classical geometrical Brownian motion.Asymptotic uniformity, Local limit theorem, Volatility

The impact of heat waves and cold spells on mortality rates in the Dutch population.

We conducted the study described in this paper to investigate the impact of ambient temperature on mortality in the Netherlands during 1979-1997, the impact of heat waves and cold spells on mortality in particular, and the possibility of any heat wave- or cold spell-induced forward displacement of mortality. We found a V-like relationship between mortality and temperature, with an optimum temperature value (e.g., average temperature with lowest mortality rate) of 16.5 degrees C for total mortality, cardiovascular mortality, respiratory mortality, and mortality among those [Greater and equal to] 65 year of age. For mortality due to malignant neoplasms and mortality in the youngest age group, the optimum temperatures were 15.5 degrees C and 14.5 degrees C, respectively. For temperatures above the optimum, mortality increased by 0.47, 1.86, 12.82, and 2.72% for malignant neoplasms, cardiovascular disease, respiratory diseases, and total mortality, respectively, for each degree Celsius increase above the optimum in the preceding month. For temperatures below the optimum, mortality increased 0.22, 1.69, 5.15, and 1.37%, respectively, for each degree Celsius decrease below the optimum in the preceding month. Mortality increased significantly during all of the heat waves studied, and the elderly were most effected by extreme heat. The heat waves led to increases in mortality due to all of the selected causes, especially respiratory mortality. Average total excess mortality during the heat waves studied was 12.1%, or 39.8 deaths/day. The average excess mortality during the cold spells was 12.8% or 46.6 deaths/day, which was mostly attributable to the increase in cardiovascular mortality and mortality among the elderly. The results concerning the forward displacement of deaths due to heat waves were not conclusive. We found no cold-induced forward displacement of deaths

Trends in mortality by labour market position around retirement ages in three European countries with different welfare regimes

<p>Objectives: In the face of economic downturn and increasing life expectancy, many industrial nations are adopting a policy of postponing the retirement age. However, questions still remain around the consequence of working longer into old age. We examine mortality by work status around retirement ages in countries with different welfare regimes; Finland (social democratic), Turin (Italy; conservative), and England and Wales (liberal).</p> <p>Methods: Death rates and rate ratios (RRs) (reference rates = ‘in-work’), 1970 s–2000 s, were estimated for those aged 45–64 years using the England and Wales longitudinal study, Turin longitudinal study, and the Finnish linked register study.</p> <p>Results: Mortality of the not-in-work was consistently higher than the in-work. Death rates for the not-in-work were lowest in Turin and highest in Finland. Rate ratios were smallest in Turin (RR men 1972–76 1.73; 2002–06 1.63; women 1.22; 1.68) and largest in Finland (RR men 1991–95 3.03; 2001–05 3.80; women 3.62; 4.11). Unlike RRs for men, RRs for women increased in every country (greatest in Finland).</p> <p>Conclusions: These findings signal that overall, employment in later life is associated with lower mortality, regardless of welfare regime.</p&gt

The Analysis of Multijet Events Produced at High Energy Hadron Colliders

We define and discuss a set of (4N - 4) parameters that can be used to analyse events in which N jets have been produced in high energy hadron-hadron collisions. These multijet variables are the multijet mass and (4N - 5) independent dimensionless parameters. To illustrate the use of the variables QCD predictions are presented for events with up to five jets produced at the Fermilab Tevatron Proton-Antiproton Collider. These QCD predictions are compared with the predictions of a model in which multijet events uniformly populate the N-body phase-space

Calculating the Expected Value of Sample Information in Practice: Considerations from Three Case Studies

Investing efficiently in future research to improve policy decisions is an important goal. Expected Value of Sample Information (EVSI) can be used to select the specific design and sample size of a proposed study by assessing the benefit of a range of different studies. Estimating EVSI with the standard nested Monte Carlo algorithm has a notoriously high computational burden, especially when using a complex decision model or when optimizing over study sample sizes and designs. Therefore, a number of more efficient EVSI approximation methods have been developed. However, these approximation methods have not been compared and therefore their relative advantages and disadvantages are not clear. A consortium of EVSI researchers, including the developers of several approximation methods, compared four EVSI methods using three previously published health economic models. The examples were chosen to represent a range of real-world contexts, including situations with multiple study outcomes, missing data, and data from an observational rather than a randomized study. The computational speed and accuracy of each method were compared, and the relative advantages and implementation challenges of the methods were highlighted. In each example, the approximation methods took minutes or hours to achieve reasonably accurate EVSI estimates, whereas the traditional Monte Carlo method took weeks. Specific methods are particularly suited to problems where we wish to compare multiple proposed sample sizes, when the proposed sample size is large, or when the health economic model is computationally expensive. All the evaluated methods gave estimates similar to those given by traditional Monte Carlo, suggesting that EVSI can now be efficiently computed with confidence in realistic examples.Comment: 11 pages, 3 figure

Diagnostic pitfalls of urogenital tuberculosis

Objectives: To describe characteristics, details of diagnosis and outcomes of urogenital tuberculosis (UGTB) in a low-prevalence country. Methods: We conducted a retrospective observational study of 37 consecutive patients diagnosed with UGTB between 1st January 2014 and 31st October 2019 in an East London hospital. Results: 68% (25/37) of patients were male and the median age was 42 years (IQR 34–55). 89% (33/37) of patients were born outside the United Kingdom with 65% (24/37) born in the South Asian region. Renal (32.4%), epididymal (24.3%) and endometrial TB (21.6%) were the most prevalent forms of UGTB. Only 13.5% of UGTB patients had concurrent pulmonary TB. The median length of time from symptom onset to treatment was 163 days, while endometrial TB had an average delay to diagnosis of 564 days. Approximately half of patients with UGTB were culture positive (51.4%). However, 70% of early morning urines (EMUs) sent in urinary TB were culture positive. 11 patients (30.6%) underwent two or more invasive procedures, such as biopsy to obtain specimen samples. The mean treatment length for all UGTB cases was 7.3 months (SD 3.1). Notably, 25% of patients with endometrial TB required surgery despite antituberculous treatment. Conclusions: UGTB is challenging to diagnose as early disease is often asymptomatic. Clinicians faced with non-specific symptoms, or features suggestive of urogenital malignancy amongst patients from TB-endemic areas, should maintain a high suspicion of UGTB