Bingo pricing: a game simulation and evaluation using the derivatives approach

The Bingo game is well known and played all over the world. Its main feature is the sequential drawing without repetition of a set of numbers. Each of these numbers is compared to the numbers contained in the boxes printed on the different rows (and columns) of the score-cards owned by the Bingo participants. The winner will be the participant that firstly is able to check all the boxes (numbers) into a row (Line) or into the entire score-card (Bingo). Assuming that the score-card has a predetermined purchase price and that the jackpot is divided into two shares, respectively for the Bingo and the Line winner, it is evident that all the score-cards show the same starting value (initial price). After each drawing, every score-card will have different values (current price(s)) according with its probability to gain the Line and/or the Bingo. This probability depends from the number of checked boxes in the rows of the score-card and from the number of checked boxes in the rows of all the other playing score-cards. The first aim of this paper is to provide the base data structure of the problem and to formalize the needed algorithms for the initial price and current price calculation. The procedure will evaluate the single score-card and/or the whole set of playing score-cards according to the results of the subsequent drawings. In fact, during the game development and after each drawing, it will be possible to know the value of each score-card in order to choose if maintain it or sell it out. The evaluation will work in accordance to the traditional Galilee's method of "the interrupted game jackpot repartition". This approach has been also mentioned by Blaise Pascal and Pierre de Fermat in their mail exchange about the "jackpot problem". More advanced objective of the paper would be the application of the stock exchange techniques for the calculation of the future price of the score-card (and/or of a set of score-cards) that will have some checked numbers after a certain number of future drawings. In the same way will be calculated the value of the right to purchase or sell a score-card (and/or of a set of score-cards) at a pre-determined price (option price). Especially during the prototyping phase, the modelling and the development of these kind of problems need the use of computational environments able to manage structured data and with high calculation skills. The software that meet these requirements are APL, J and Matlab , as for their capability to use nested arrays and for the endogenous parallelism features of the programming environments. In this paper we will show the above mentioned issues through the use of Apl2Win/IBM . The formalisation of the game structure has been made in a general way, in order to foresee particular cases that act differently from the Bingo. In this way it is possible to simulate the traditional game with 90 numbers in the basket, 3 rows per 10 columns score-cards, 15 number for the Bingo and 5 numbers for the Line but already, for example, the Roulette with 37 (or 38) numbers, score-cards with 1 (or more) row and 1 column and Line with just 1 number.bingo, options, futures, gambling, market, evaluation

Volatility and stock market direction: a study on emerging markets.

Volatility indices, such VIX, can be used for determining stock market direction. In this paper, we analyze the relationship between changes in the VIX direction and changes in the turning point of S&P 500 and the MSCI Latin-America Emerging Market index, in order to see whether they anticipate the changes. Also, the volatility of emerging markets measured by standard deviation and their relationship with the stock market movements within this market are calculated, since the greater the value of the volatility, the greater the likelihood of a rise or fall. In order to locate the turning point and the upward and downward phases of the cycles, empirical methods are applied and are characterized by using a set of decision rules that reflect the practical experience gained by analysts. Our conclusions include: Turning points, or peaks and troughs, in the VIX are coincident with peaks and troughs in the opposite direction for the S&P 500 index and in emerging markets

Constraints on deviations from Λ{\Lambda}CDM within Horndeski gravity

Recent anomalies found in cosmological datasets such as the low multipoles of the Cosmic Microwave Background or the low redshift amplitude and growth of clustering measured by e.g., abundance of galaxy clusters and redshift space distortions in galaxy surveys, have motivated explorations of models beyond standard $\Lambda$CDM. Of particular interest are models where general relativity (GR) is modified on large cosmological scales. Here we consider deviations from $\Lambda$CDM+GR within the context of Horndeski gravity, which is the most general theory of gravity with second derivatives in the equations of motion. We adopt a parametrization in which the four additional Horndeski functions of time $\alpha_i(t)$ are proportional to the cosmological density of dark energy $\Omega_{DE}(t)$. Constraints on this extended parameter space using a suite of state-of-the art cosmological observations are presented for the first time. Although the theory is able to accommodate the low multipoles of the Cosmic Microwave Background and the low amplitude of fluctuations from redshift space distortions, we find no significant tension with $\Lambda$CDM+GR when performing a global fit to recent cosmological data and thus there is no evidence against $\Lambda$CDM+GR from an analysis of the value of the Bayesian evidence ratio of the modified gravity models with respect to $\Lambda$CDM, despite introducing extra parameters. The posterior distribution of these extra parameters that we derive return strong constraints on any possible deviations from $\Lambda$CDM+GR in the context of Horndeski gravity. We illustrate how our results can be applied to a more general frameworks of modified gravity models.Comment: 22 pages; 4 figures; 9 tables. The constraints have been revised to match the precision required according to the recently released hi_class pape

Stock Market Crisis in Spain and their Comparison with Other International Market: Analysis of the Principal Characteristics

Periódicamente en los mercados bursátiles se producen periodos de caídas drásticas que son denominados como “crisis bursátiles”. El análisis de estas crisis sobre el mercado bursátil Español y sus repercusiones, puede permitir a gestores e inversores anticipar sus estrategias ante las mismas. Las variables empíricas más importantes que definen a una crisis, las cuales serán objeto de este estudio, son el porcentaje de caída desde el máximo, la duración de la caída y el tiempo necesario hasta recuperar el máximo anterior. La comparación de estas variables con las obtenidas del análisis de los mercados Americano, Alemán e Inglés, nos permitirá ver el grado de correlación entre crisis a nivel internacional y realizar previsiones.Regularly there are periods of a dramatic decline in stock markets that are defined as “stock market crashes” and cause “stock market crisis”. Analysis of the influence of this crisis over the Spanish stock market and their repercussions can enable stockbrokers and investor to use anticipating strategies. The most outstanding empirical variables which define a crisis, which are the object of this study, are the maximum drawndown percentage, de duration of the decline and the recovery time. The comparison of these variables with those obtained from the American, German and English markets analysis allows us to see the degree of correlation between these crises and to do forecasting

Evaluating the effectiveness of the Emergency Neurological Life Support educational framework in low-income countries.

BackgroundThe Emergency Neurological Life Support (ENLS) is an educational initiative designed to improve the acute management of neurological injuries. However, the applicability of the course in low-income countries in unknown. We evaluated the impact of the course on knowledge, decision-making skills and preparedness to manage neurological emergencies in a resource-limited country.MethodsA prospective cohort study design was implemented for the first ENLS course held in Asia. Knowledge and decision-making skills for neurological emergencies were assessed at baseline, post-course and at 6 months following course completion. To determine perceived knowledge and preparedness, data were collected using surveys administered immediately post-course and 6 months later.ResultsA total of 34 acute care physicians from across Nepal attended the course. Knowledge and decision-making skills significantly improved following the course (p=0.0008). Knowledge and decision-making skills remained significantly improved after 6 months, compared with before the course (p=0.02), with no significant loss of skills immediately following the course to the 6-month follow-up (p=0.16). At 6 months, the willingness to participate in continuing medical education activities remained evident, with 77% (10/13) of participants reporting a change in their clinical practice and decision-making, with the repeated use of ENLS protocols as the main driver of change.ConclusionsUsing the ENLS framework, neurocritical care education can be delivered in low-income countries to improve knowledge uptake, with evidence of knowledge retention up to 6 months