Estimating the truncation error in the case of solving one dimensional Black-Scholes equation

In the early 1970s, Fischer Black and Myron Scholes made a breakthrough by deriving a differential equation that must be satisfied by the price of any derivative security dependent on a non-dividend-paying stock. They used the equation to obtain the values for European call and put options on the stock. Options are now traded on many different exchanges throughout the world and are very popular instruments for both speculating and risk management. There are several approaches to option pricing but however we only consider Partial Differential Equations(PDE) approach, where options are expressed as solutions to certain partial differential equations. These equations are specified over an infinite(unbounded) region and usually cannot be solved exactly. Most numerical methods for solving partial differential equations require the region to be finite, so before applying numerical methods the problem is changed from infinite to finite region. The aim of our thesis is to study the error caused by this change, will do that by estimating the error at the boundaries and use these estimates to get pointwise error inside the domain, followed by numerical verification. The structure of the thesis is as follows: Chapter one provides a brief introduction of option pricing and includes neccesary results. In chapter two we give a defination of maximum principle for backward parabolic equations and prove some lemmas based on this principle which will be useful throughout this thesis. We further outline ways of getting estimates with the aid of the results we got in our lemmas. In chapter three we will obtain estimates at the truncation boundaries for both call and put option. In chapter four we use the estimates of the previous chapter to find the estimates inside the region. In chapter five we demonstrate the process of using our estimates in the case of pricing concrete put and call options and show the validity of the estimates by finding numerically the values of the solution of this truncated problem

An assessment of external HIV-related stigma in South Africa: implications for interventions

Background Globally, external HIV-related stigma is a major threat to all HIV prevention, care and treatment interventions including the recently launched Universal Test and Treat (UTT) strategy in South Africa and the 90-90-90 targets set by UNAIDS for the global response by 2020. The 90-90-90 targets are put in place to track the progression from HIV testing to durable viral load suppression among people living with HIV. The targets guide HIV programmes to achieve 90% known HIV status, to access 90% antiretroviral therapy and to suppress 90% viral loads (UNAIDS, 2017). Achievement of the 90-90-90 targets has since become a part of South Africa's National Strategic Plan for HIV, TB and STIs 2017-2022. External HIV-related stigma in this study was defined as the presence of one or more of the following attitudes and behaviours: rejection, avoidance, intolerance, stereotyping, discrimination, and physical violence towards people living or perceived as having HIV. There have not been many efforts to attenuate HIV-related stigma in South Africa, as it continues to exist. There has been a scale up of other HIV responses, such as HIV Counselling and Testing (HCT) and treatment, with the argument made that in scaling up these biomedical approaches, stigma would disappear. Furthermore, its exact magnitude, trends over the years and correlates have not been explored fully at national level, hence the present study known as Stigma Assessment Study in South Africa (SASSA). SASSA is based on the Institutional Social Construction theory framework. It explores the external HIV-related stigma magnitude and its trends between 2005 and 2012, as well as the associated factors which influence its prevalence in South Africa at a national level. The study further explores the mediating and moderating factors of external HIV-related stigma and tries to explore external HIV-related stigma by viewing individuals with HIV living in families, societies and structures, with the hope of contributing to the development of new systematic HIV-related stigma interventions in South Africa as well as, strengthening existing ones. Methodology The project used secondary data obtained from three South African national population HIV surveys which were conducted in 2005, 2008 and 2012 by a research consortium led by the Human Sciences Research Council. Sub-samples of the original surveys consisting of respondents aged 15 years and older who had responded to the stigma questions in the three surveys were extracted and included in the SASSA analysis. A nationally representative sample of a total of 16 140 individual respondents from the 2005 survey, 13 134 from the 2008 survey and 30 748 from the 2012 survey was used in the study. Two different measures of external HIV stigma are used in this analysis, one is a summary measure from the latest survey data, i.e. 2012, which was used to do a regression analysis. The summary measure was regarded as reliable to use for the regression analysis as it provides crude effect of the exposure factors on external HIV stigma. However, this summary measure was not included in the previous surveys, i.e. 2005 and 2008, and therefore could not be used for trends analysis. We therefore used 4 individual stigma items for the trends analysis as these were included in all 3 surveys. The use of 4 individual stigma items was important because when data from a variety of sources or categories have been joined together, the meaning of the data can be difficult to see. It was therefore considered ideal to assess the performance of the individual constructs on their individual contribution to the impact on HIV external stigma. Furthermore, analysis using individual constructs provided an opportunity to see specific patterns which could have remained obscure in crude analysis. The first measure of external HIV-related stigma used in the regression analysis was measured by five individual items which elicited attitudes towards people living with HIV (PLHIV). The five items were based on a 9-item scale that was originally developed and tested in a South African population, and the 9-item scale was found to be internally consistent (alpha = 0.75) and reliable (r = 0.67). The 5 items were (1) People who have AIDS are dirty; (2) People who have AIDS are cursed; (3) People who have AIDS should be ashamed; (4) People with AIDS must expect some restrictions on their freedom; (5) A person with AIDS must have done something wrong and deserves to be punished. As explained above, the specific external HIV stigma patterns second measure, which was utilized to explore stigma trends over the years 2005, 2008 and 2012, consists of four individual stigma items which elicited attitudes towards PLHIV. The four individual stigma items included: (1) If you knew that a shopkeeper or food seller had HIV, would you buy food from them? (2) Would you be willing to care for a family member with AIDS? (3) Is it a waste of money to train or give a promotion to someone with HIV/AIDS? (4) Would you want to keep the HIV positive status of a family member a secret? Findings Overall, external HIV-related stigma was found to exist among 38.3% of adult South Africans in 2012. Multiple regression analysis showed that predictors of external HIV-related stigma were race, sex, education level, self-perceived risk of HIV infection and HIV knowledge (p< 0.01). Females were less likely to report external HIV-stigma than males (AOR = 0.9, P< 0.001). Those who perceived themselves to be at high risk of HIV infection were less likely to display some stigma than those who believed they were at low risk (AOR = 0.89, p < 0.01). The study did not find any significant associations between HIV testing or awareness of HIV status, with external HIV-related stigma in this study. Looking at the individual external HIV stigma items used to measure trends, the study reveals a slight decrease in the reporting of stigma over the three time periods (2005 vs 2008 vs 2012) on responses for two of the stigma items (Q1: If you knew that a shopkeeper or food seller had HIV, would you buy food from them, and Q2: Would you be willing to care for a family member with AIDS). While an increase was observed in the reporting of stigma over the three years on responses for two of the stigma items (Q3: Is it a waste of money to train or give a promotion to someone with HIV/AIDS, and Q4: Would you want to keep the HIV positive status of a family member a secret). The structural equation modelling (SEM) showed likelihood ratio test results with a p-value greater than 0.05, a root mean square error of approximation (RMSE) of 0.008 and Tucker–Lewis index (TLI) value of 0.985. The model fit assessment results allow us to accept that an hypothesized model of the study is not far from a perfect model. The SEM results also showed a direct effect of sex on HIV knowledge statistically significant at p < 0.001, with race having an effect of 3.3% and education a direct effect of 9.5%, and both of these showed a statistically significant effect (p < 0.001) respectively. HIV knowledge showed to have a statistically significant inverse relationship on external HIV stigma of -10.4% (95% CI: -12.3-0.09) p< 0.001. Awareness of HIV status had the highest positive direct effect on external stigma of 10% (95% CI: 4.41-15.67%) p<0.001. With regard to indirect effects, sex, race, and education had minimal negative indirect effects on external stigma, which was statistically significant for all the three covariates. With the said effects of external HIV-related stigma, it was found that HIV knowledge independently mediates the relationship between Level of Education, Awareness of HIV status, Race, HIV testing history, and Sex, with External HIV-related stigma. Conclusion External HIV-related stigma still exists in South Africa despite previous success in massive ART rollout, HTC campaigns, and most recently test-and-treat programmes, which were arguably thought to have a parallel effect in the decrease of HIV related stigma. The focus on individualistic health structural approaches that do not generally have stigma-reduction as a specific aim, as discussed, is likely to undermine the successes achieved in the fight against HIV thus far. There is a need to develop innovative holistic interventions which are specifically intended for HIV stigma reduction. These should be inclusive of both social institutional elements and health structural elements to address the challenge of external HIV-related stigma

Women's views on and experiences of condom use : an exploration of how this impacts on women's sexual satisfaction and male condom use among women

Includes bibliographical references.Consistent condom use amongst women and men is one of the important safer sexual practices in combating the spread of HIV/AIDS. This dissertation examines factors which hinder or facilitate consistent male condom use, particularly as it relates to women's sexual satisfaction. Findings indicated that women felt that it was important to use condoms during sexual intercourse in order to obtain protection against HIV, STIs and pregnancy. Just over half of the women reported condom use at last sexual intercourse. Women's own sexual dissatisfaction was regarded as one of the main reasons why condoms were not consistently used by women. The results of this study suggest that that while it is important for HIV/AIDS interventions to focus it is also important to better understand a less investigated issue of women's own possible resistance to male condom use

Partial oxidation of ethanol over vanadium iron antimonate catalysts

Bibliography: p. 151-161.VSbO₄ and FeSbO₄ are proven catalysts for the amm(oxidation) of propane/propylene. These catalysts systems have been shown to possess over-oxidation limiting characteristics. Ethanol oxidation is carried out in two-staged processes industrially, mainly because of the challenges presented by over-oxidation of the intermediates to carbon oxides

Non-Saccharomyces Killer Toxins: Possible Biocontrol Agents Against Brettanomyces in Wine?

Red wine spoiled by the yeast Brettanomyces bruxellensis is characterised by off-odours commonlydescribed as horse sweat, phenolic, varnish and band-aid. The growth of this yeast in wine is traditionallycontrolled by the use of sulphur dioxide (SO2). However, the concentration of SO2, the pH of the wine,the presence of SO2-binding chemical compounds in the wine, as well as the strain of B. bruxellensis,determine the effectiveness of SO2. Other chemical preservatives have been tested, but are not much moreefficient than SO2, and methods used to clean barrels are only partially effective. Filtration of wine andthe use of electric currents/fields are also reported to alter the physical and sensory properties of wine. Inthis context, alternative methods are currently sought to achieve full control of this yeast in wine. Killertoxins have recently been proposed to fulfil this purpose. They are antimicrobial compounds secretedby Saccharomyces and non-Saccharomyces yeasts, displaying killer activity against other yeasts andfilamentous fungi. They are believed to play a role in yeast population dynamics, and this killer phenotypepotentially could be exploited to inhibit the growth of undesired microorganisms within a microbialecosystem such as that occurring in wine. In this review, non-Saccharomyces killer toxins are describedand their potential application in inhibiting B. bruxellensis in wine is discussed in comparison to othertried methods and techniques

The readiness for m-government in a South African provincial government

Masters of CommerceThis study aims at determining the m-Readiness of a Province for m-Government from a context of its Provincial Government (PG), the underprivileged citizens of the region and the mobile fluency thereof. In answering the research question, i.e., “What is the extent of readiness of the government and that of the underprivileged citizens for introduction of m-Government within the region under study”, literature was reviewed and existing models synthesised, and from that, a conceptual model was presented which acted as a reference point. The research process used a quantitative method and utilised a stratified random sampling method in determining and adequately representing the populations under study, namely, underprivileged citizens and IT managers and specialists from the PG’s office. Descriptive statistics were adopted in analysing the collected data used in answering the research questions and findings presented. The findings show that the Province is m-Ready for m-Government services, from the studied contexts of the PG, underprivileged citizens and mobile fluency. The reference model, that is, the Provincial Mobile Readiness Measurement Model (PMRMM), was developed from a perspective of the Province under study, therefore, its theoretical generalizability to other Provinces has to be first studied before being implemented. Secondly, the study only looked at three segments of the government service delivery value chain, which are the Government-to-Citizen (G2C), Government-to-Employee (G2E) and Governmentto- Government (G2G). The contributions of the study are twofold, firstly as a practical decision-making guide regarding introduction of m-Government and secondly, it adds to the conceptual understanding of government readiness for introduction of government services via ICT mobile platforms

Screening Non-Saccharomyces Yeasts as Low Ethanol Producing Starter Cultures

Non-Saccharomyces yeasts are known for their low fermentation rate in comparison to Saccharomyces cerevisiae.&nbsp; In this study, non-Saccharomyces yeasts were inoculated into Chenin blanc grape must and fermented under aerobic and anaerobic conditions.&nbsp; Saccharomycodes ludwigii displayed a strain-dependent fermentation rate, which yielded between 5.2% and 9.9% ethanol concentration under both conditions, albeit with residual sugar.&nbsp; Aerobic conditions favoured the production of reduced ethanol which was between 5.8% and 9.7% for non-Saccharomyces yeasts in comparison to S. cerevisiae (10%).&nbsp; This trend was observed for Wickerhamomyces anomalus, Stamerella bacillaris (Candida zemplinina), Metshnikowia pulcherrima, Cyberlindnera saturnus, Wickerhamomyces subpelliculosus and Cyberlindnera jadinii.&nbsp; The laboratory-scale wines prepared with the aforementioned yeasts yielded ripe fruit and floral aroma attributes while other non-Saccharomyces yeasts resulted in wines with spicy, acidic and solvent aroma notes

Nutritional quality of wet and dry processed Moringa oleifera Lam. leaves : a review

Moringa oleifera: Lam. is a plant species that has found a multitude of applications from health, water clarification and as a food source. In particular, the tree leaves have been consumed in various countries were it is incorporated in the local diet. The advent of food processing technologies have alluded to various methods to process, preserve and extend the shelf-life of fresh produce. This review focuses on the nutrient quality of M. oleifera leaves processed using energy-efficient processing technologies such as sun drying, blanching, boiling and fermentation.The National Research Foundation.https://www.tandfonline.com/loi/lfri20hj2023Consumer ScienceFood Scienc

Yeast derived metabolites and their impact on nutritional and bioactive properties of African fermented maize product

DATA AVAILABILITY : The research data is from literature sources.Fermented foods are an integral part of the diet for many communities in Africa. The fermentation of maize is characterized by an improved nutrient content/bioavailability and the presence of bioactive compounds which are largely attributed to the activity of the microbial population mainly lactic acid bacteria (LAB) and yeasts. The role of LAB in maize and other cereal fermentations has been extensively studied. However, limited literature is available on the role of yeasts in maize fermentations and resultant nutritional and health promoting properties. This review explores the contribution of yeasts to the nutritional and health properties of fermented maize and other cereal products. Additionally, the proliferation and growth characteristics of dominant yeasts and their derived metabolites are discussed. It is particularly important to comprehend the processes and type of yeasts involved in maize fermentation as an essential step in maize product development. This will facilitate the development of yeast-based starter culture, improve maize fermentation process and provide better understanding of associated nutrition and bioactive properties.The National Research Foundation of South Africa.https://www.elsevier.com/locate/fbiohj2024Consumer ScienceFood ScienceSDG-02:Zero Hunge

Effects of combining microwave with infrared energy on the drying kinetics and technofunctional properties of orange-fleshed sweet potato

DATA AVAILABILITY : The underlying data of the results supporting the study are stored at the University of Pretoria database.The aim of the study was to determine the effects of oven, microwave (MW), and infrared (IR) drying technology on the drying kinetics, physicochemical properties, and β-carotene retention of the dried orange-fleshed sweet potato flour (OFSP). Fresh OFSP slices were dried in an oven (40°C), MW (80 W), IR (250 W), MW-IR (80 W + 250 W), and freeze-drying (-45°C, 100 kPa) and milled into flour. Hot air at a constant temperature was applied to all thermal drying technologies (40°C, 4.5 m/s air velocity). The drying rate of the MW-IR drying method was the fastest (45 min), followed by MW (60 min), IR (120 min), and oven (180 min). The Page model was most suitable for the oven-drying method, the Lewis model for IR drying, and Henderson and Pabis for IR and Logarithmic for the MW-IR method. The pasting and thermal properties of the flours were not significantly (p > 0.05) affected by the different drying methods. However, IR- and MW-IR-dried flours showed a higher final viscosity when compared to other drying methods. MW-IR drying methods, IR, and MW showed a higher water solubility index, while the oven and freeze-drying methods showed a lower solubility index. MW-IR drying methods showed a higher retention of β-carotene (85.06%). MW also showed a higher retention of β-carotene (80.46%), followed by IR (66.04%), while oven and freeze-drying methods showed a lower retention of β-carotene. High β-carotene retention in the produced flour is due to the faster drying method, and these flours can be used in food-to-food fortification to address vitamin A deficiency.The European Union’s Horizon 2020 research and innovation programme and DSI-NRF CoE in Food Security. Open Access funding was enabled and organized by SANLiC Gold.https://ifst.onlinelibrary.wiley.com/journal/17454549hj2024Consumer ScienceFood ScienceSDG-02:Zero Hunge