South Africa is characterised as having high unemployment rates, low GDP forecast growth rates and a high percentage of the population living in rural areas. Therefore, the research explored the ability of microfinance, using the Grameen Bank model, to increase economic development in the rural areas of South Africa. Grameen Bank is considered to be the mother of conscience driven microfinance. The Bank's approach to poverty alleviation provides the poor with direct access to micro loans in order to increase their earnings from productive self-employment activities. Among other things, the loans are characterised as being advanced to small groups without the requirement of collateral. These loans are considered to have helped to alleviate poverty and increase physical and human resources, and confirm that poverty alleviation and human resource development is possible with targeted credit (Khandker, 1996). The model has been successful in improving the livelihoods of the borrowers using various measures such as providing the ability to afford three meals a day, electricity in their homes and to educate their children. In addition, borrowers are able to grow business and create employment in their communities. Although the Grameen Bank model has been successfully applied throughout the world, it has attainted limited success in South Africa. The business model has not been able to achieve operational or financial sustainability due to high staff and regulatory costs in relation to other emerging markets compounded by the inability to utilise borrower savings. In addition, borrowers are unable to create microenterprises that effectively compete with the formal economy. Microfinance institutions could address operational inefficiency by making use of the community based lending structures already operating under the Grameen philosophy, known as stokvels, and by embracing cell phone technology. In addition, institutions that provide social upliftment should focus on the skills training required by entrepreneurs to operate more successfully and for the employee to be more employable. The Grameen Bank model is not a panacea for South African growth based poverty alleviation. However, when combined with wide reaching economic and social policies, microfinance may assist in the creation of long term economic growth and social upliftment while improving the current lives of the poor.

M.A. / In South Africa, high unemployment rates, uneven distribution of opportunities and poverty are major concerns for the government. Poverty is defined as the deprivation of people due to the lack of access, and their right, to certain commodities. In 2004, close to 15,4 million people were living below the poverty line. In addition to this, in 2005, 53 percent of South Africans, equating to 16,4 million persons, were excluded from formal financial services. Microcredit has been advocated as a tool to reduce poverty. A world renowned microfinance model, the Grameen Bank model of Bangladesh has had success in not only reducing poverty, but also allowing poor people access to formal financial services. The bank has 7,93 million borrowers, with 97 percent being female clients, and one third of its borrowers have crossed the poverty line. Four organisations in South Africa have replicated this model. These organisations are the Small Enterprise Foundation, Marang Financial Services, The Women's Development Businesses, and the South African National Zakah Fund. These organisations have achieved in reaching 130,000 clients across South Africa, and extended over R1 billion in loans. However, only four of the nine provinces in the country have been infiltrated effectively. The impacts on these borrowers lives, and their households has been exceptional. Many of the families now have increased selfworth, a stable income, job security and access to credit in order to advance their businesses. In addition, Grameencredit has allowed thousands of South Africans access to legal, formal financial services. Thus, Grameencredit has been advocated to be an effective method in the fight against poverty.

Diese Dissertation wendet eine unendlichdimensionalen Markov'schen Hebemethode auf nicht-Markov'sche Dynamiken an und schlägt das Modell der kontinuierlichen Saatbank sowie ein unendlichdimensionales Preisbeeinflussungsmodell vor. Wir verallgemeinern das Saatbankmodell aus [BGCKWB16], um allgemeinere Dormanzzeitverteilungen zu berücksichtigen. Inspiriert von [GdHO22] führen wir die Wright-Fisher-Diffusion und Koaleszenz mit einer Kontinuität von Saatbänken ein. Durch die Formulierung einer unendlichen dimensionale stochastischen Differentialgleichung beweisen wir die Existenz einer eindeutigen starken Lösung: der kontinuierlichen Saatbank-Diffusion. Anschließend zeigen wir, dass dieser Diffusionsprozess das Skalierungs-Limit der Allelfrequenzprozesse in einer Reihe von diskreten Wright-Fisher-Modellen darstellt. Darüber hinaus stellen wir eine Dualitätsbeziehung zwischen der kontinuierlichen Saatbank-Diffusion und der kontinuierlichen Saatbank-Koaleszenz her und diskutieren einige grundlegende Eigenschaften dieses Koaleszenzprozesses. Im finanziellen Bereich entwickeln wir, ähnlich wie im kontinuierlichen Saatbankmodell, einen unendlichen transienten Preisbeeinflussungsprozess. Dieser Prozess ist ein Markov'sche Hebung eines nicht-Markov'schen 1-dimensionalen Preisbeeinflussungsprozesses. In einem additiven Preisbeeinflussungsszenario vereinfachen wir, entsprechend den Methoden in [AKU22] und [BB24], das Problem der optimalen Liquidation zu einem linearen-quadratischen Optimalsteuerproblem. Strafterm werden in das erwartete Kostenfunktional eingeführt, um die eindeutige Lösbarkeit sicherzustellen. Schließlich stellen wir in Szenarien wie multiplikativen Preisbeeinflussungen die Skorokhod M1-Kontinuität der Kosten im unendlichen Dimensionen-Setting sicher. / This thesis applies an infinite-dimensional Markovian lifting method to non-Markovian dynamics, proposing the continuum seed-bank model and an infinite-dimensional price impact model. We generalize the seed-bank model from [BGCKWB16] to accommodate more general dormancy time distributions. Inspired by [GdHO22], we introduce the Wright-Fisher diffusion and coalescent with a continuum of seed-banks. By formulating an infinite-dimensional stochastic differential equation, we prove the existence of a unique strong solution: the continuum seed-bank diffusion. We then show that this diffusion process is the scaling limit of allele frequency processes in a sequence of discrete-time Wright-Fisher type models. Furthermore, we establish a duality relation between the continuum seed-bank diffusion and the continuum seed-bank coalescent, and discuss some basic properties of this coalescent process. In the financial domain, akin to the continuum seed-bank model, we develop an infinite-dimensional transient price impact process. This process is a Markovian lift of a non-Markovian 1-dimensional price impact process. In an additive price impact scenario, following the methods in [AKU22] and [BB24], we simplify the optimal liquidation problem to a linear-quadratic optimal control problem. Penalty terms are introduced into the expected cost functional to ensure unique solvability. Finally, in scenarios such as multiplicative price impacts, we establish the Skorokhod M1 continuity of the cost in the infinite-dimensional setting.