Thesis (M.C.A.)--Victoria University of Wellington, 2009. / Includes bibliographical references.

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

We present a tree algorithm, called the willow tree, for financial derivative pricing. The setup of the tree uses a fixed number of spatial nodes at each time step. The transition probabilities are determine by solving linear programming problems. The willow tree method is radically superior in numerical performance when compared to the binomial tree method.

The Zero-Coupon Inflation Indexed Swap (ZCIIS) is a derivative contract through which inflation expectations on the Consumer Price Index (CPI) are actively traded in the US. In this thesis we consider different ways to use the information from the ZCIIS market for modeling forward inflation in a risk-neutral framework. We choose to implement a model using a Monte Carlo methodology that simulates the evolution of the forward CPI ratio. We prefer this approach for its flexibility, ease of implementation, instant calibration to the ZCIIS market and intrinsic convexity adjustment on the inflation-linked payoff. Subsequently, we present a series of results we obtain when modeling a chain of consecutive CPI ratios for simulating the evolution of spot inflation. Furthermore, we use this for pricing inflation caplets and floorlets. Finally, we use the intuition gained from this exercise to analyse our results for pricing inflation caps.

Minestery of Education of Lithuania, besides “Programme”, in 1994 offered for all schools methodical recommendations for educational process, named “General Educational Standards”. The process has influenced on citizens’ educational of Independent Lithuania. The Standards have allowed looking at subject in a new way. The topic of the given MA work “Teaching of mathematics analysis of elements in Lithuania since 1991”. Work goal is to clarify peculiarities of teaching of mathematics analysis of elements: -To consider the following topics: function, derivative, line, integral. Tasks: 1.To consider teacher’s job in our days and to find out this role in Educational process, to discuss connection between pupil and teacher. 2.To answer the question “What is integration and intersubject relations”. 3.To announce mark’s norms at lessons of mathematics. The given work is an analysis of text books, didactic books, small pedagogical experiments and statistic analysis. In general, to find the answer “How to teach and to be tought?

In this dissertation, we investigatethe supersymmetric completion of curvature squared invariants in five and six dimensionsas well as the construction of off-shell Poincar´e supergravities and their matter couplings. We use superconformal calculus in fiveand six dimensions, which are an off- shell formalisms. In fivedimensions,there are twoinequivalentWeyl multiplets: the standard Weyl multiplet and the dilaton Weyl multiplet.The main difference betweenthese twoWeyl multiplets is thatthe dilaton Weyl multipletcontains a graviphoton in its field content whereas the standard Weyl multiplet does not.A supergravity theory based on the standard Weyl multiplet requires coupling to an external vector multiplet. In five dimensions,we construct two new formulations for 2-derivative off-shell Poincar´e supergravity theories and present the internally gauged models. We also construct supersymmetric completions of all curvature squared terms in five dimensional supergravity with eight supercharges.Adopting the dilaton Weyl multiplet, we construct a Weyl squared invariant, the supersymmetric combination of Gauss-Bonnet combination and the Ricci scalar squared invariant as well as all vector multiplets coupled curvature squared invariants. Since the minimal off-shell supersymmetric Riemann tensor squared invariant has been obtained before, both the minimal off-shell and the vector multiplets coupled curvature squared invariants in the dilation Weyl multiplet are complete. We also constructedan off-shell Ricci scalar squared invariant utilizing the standard Weyl multiplet.The supersymmetric Ricci scalar squared in the standard Weyl multiplet is coupled to n number of vector multiplets by construction, and it deforms the very special geometry. We found that in the supersymmetric AdS5 vacuum, the very special geometry defined on the moduli space is modified in a simple way. We study the vacuum solutions with AdS2 × S3 and AdS3 × S2 structures. We also analyze the spectrum around a maximally supersymmetric Minkowski5, and study the magnetic string and electric black hole. Finally, we generalize our procedure for the construction of an off-shell Ricci scalar squared invariant in five dimensions to N = (1, 0), D = 6 supergravity.

The objective of this research proposal is to explore the extent to which credit derivatives can be used effectively by domestic financial institutions, in particular, Commercial Banks to hedge the credit risk associated with lending to the Small, Medium and Micro enterprise (SMME) market segment, thereby making lending to this market segment an attractive and viable banking proposition. The financial services sector in South Africa has come under severe criticism from Government, trade unions and the unbanked, low income earners for not fulfilling their social responsibility, in terms of, not banking the Small, Medium and Micro enterprise (SMME) customer base. In particular, financial institutions have been accused of ignoring or not giving sufficient attention to the financial/credit needs of this market segment. These parties have argued that many of the domestic financial institutions are applying standard credit criteria to this market segment, which they feel is incorrect. This has often resulted in SMME's having their requests for credit facilities declined by domestic financial institutions and then having to resort to approaching unscrupulous "loan sharks" for credit facilities, which facilities are often made available to them at exorbitant interest rates. The alleged reluctance on the part of domestic financial services institutions to make available credit facilities, in the form of start-up business loans and asset-based finance to the SMME segment has possibly hindered economic growth, productivity, employment and resulted indirectly in a host of other social anomalies. Alister Ruiters of the Department of Trade and Industry has been publicly vociferous in his attack on domestic financial institutions (Business Day, August18, 1999). It would appear these financial institutions are only prepared to do business with this market segment in partnership with Government, where Government bears a large proportion of the risk by providing guarantees or indemnities on behalf of the client. Examples of such guarantees include Khula and Sizabantu guarantees issued by agencies controlled within the ambit of the Department of Trade and Industry. Financial service institutions have defended their actions by countering that the credit risk attached to making loans available to the SMME market segment is often unacceptable to them. Many of these potential clients are characterised by adverse credit records, show little stability, in terms of, employment and domicilium and often do not have any tangible collateral available to support their loan requests. That is, the risk from lending to this market segment far outweighs the potential returns. Further, these financial institutions have argued that with South Africa having been accepted into the international fold and following the accelerated pace of globalisation, new markets have opened up for their shareholders. Hence, shareholders are requiring improved returns (capital gains and/or dividends); else they are at liberty to move their funds to other investment destinations. The pressure on domestic financial institutions to deliver consistently better returns on equity has been and continues to be a difficult one. This is exacerbated by the increasing competitive pressure from both retail competitors who are now offering financial services, such as Pick 'n Pay Financial Services, Woolworth's, and foreign financial institutions, who have entered the domestic scene. For many of the retail competitors the offering of financial services is seen merely as an extension of their product line. Existing infrastructure, in the form of, branches /outlets and technology are largely already in place. Further, they are not bound by the same liquidity reserve requirements imposed by the South African Reserve Bank (SARB), as are the domestic financial institutions they now compete against. Hence, the retail competitors' profit margins are likely to be higher. Further, as many of the foreign financial institutions are not constrained by the same social responsibility obligations local financial institutions face and as they have not invested substantially in branch networks and other infrastructure in South Africa, their profit margins are higher and hence their returns on equity is likely to be significantly higher than the domestic financial institutions. Following the increasing popularity of Credit Derivatives in countries, such as, the United States of America, the United Kingdom and India, it is my intention to explore whether this instrument can be used effectively by domestic financial institutions as an hedging tool to insure against what they might otherwise consider unacceptable risk in the SMME market segment. That is, will the use of credit derivatives make the lending of funds to this client base an acceptable or attractive proposition to domestic financial institutions. However, we first need to define credit risk and credit derivatives before we proceed further. Creditex (Commentary, May 2001) defines credit risk as: "the risk of loss following default. " PriceWaterhouseCoopers defines a credit derivative as : "a credit risk management instrument that allows a financial institution to transfer credit risk to another party". Having, in simple terms, defined what we mean by credit risk and credit derivatives, we proceed by suggesting how credit derivatives can be used as an effective hedging tool and also some of the possible shortcomings that may be associated with the use of credit derivatives in South Africa. Cheow and Chiu (Managing Credit Risks, May 23,2001) suggest credit derivatives have the potential to transform the way in which Commercial Banks do business. The impact of credit derivatives is likely to result in changes in Bank's operating and credit models of assessment, pricing policies and offer insight into how products and services may be developed and implemented. Traditionally Banks appear to have been involved in all aspects of lending from origination to administration, monitoring and collection. These authors suggest the resulting credit model emanating from the use of credit derivatives is likely to only concentrate on origination of the loan with the view of later selling-off the book itself or insuring the credit risk. This latter alternative involves credit derivatives. We turn our attention to highlighting some possible constraints to the effective use of credit derivatives in South Africa. These are as follows :  Lack of effective infrastructure  Lack of liquidity  Lack Of Transparency  Restrictive Central Bank regulations and exchange controls  limited number of large financial institutions. / Thesis (MBA)-University of Natal, Durban, 2002.

Atypical gene expression has a major influence on the disease profile of several severe human disorders. Oligonucleotide (ON) based therapeutics has opened an avenue for compensating deviant protein expression by acting on biologically important nucleic acids, mainly RNAs. Antisense ONs (asONs) can be designed to target complementary specific RNA sequences and thereby to influence the corresponding protein synthesis. However, cellular uptake of ONs is poor and is, together with the target specificity of the asONs, the major limiting factor for the development of ON based therapeutics. In this thesis, the mechanisms of well-characterized cell-penetrating peptides (CPPs) are evaluated and CPPs are adapted for cellular ON-delivery. The functionality of ON derivatives in cells is investigated and by optimization of asONs, targeting pre-messenger RNA, high efficiency and specificity is achieved. The optimization of the asONs is based on sequence design and through the choice of nucleic acid analogue composition. It is concluded that asONs, partly composed of locked nucleic acids are attractive for splice-switching applications but these mixmers must be designed with limited number of locked nucleic acid monomers to avoid risk for off-target activity. A protocol allowing for convenient characterization of internalization routes for CPPs is established and utilized. A mechanistic study on cellular CPP uptake and translocation of associated ON cargo reveals the importance of the optimal combination of for example charge and hydrophobicity of CPPs for efficient cellular uptake. Formation of non-covalent CPP:ON complexes and successful cellular delivery is achieved with a stearylated version of the well-recognized CPP, transportan 10. The results illustrate that CPPs and ON derivatives have the potential to become winning allies in the competition to develop therapeutics regulating specific protein expression patterns involved in the disease profile of severe human disorders. / At the time of doctoral defense, the following papers were unpublished and had s status as follows: Paper 4: Accepted.Peper 5: In press. / VINNOVA-SAMBIO Multidisciplinary BIO

In this thesis, we have considered two important problems, Boolean satisfiability (SAT) and derivative free optimization in the context of large scale quantum computers. In the first part, we survey well known classical techniques for solving satisfiability. We compute the approximate time it would take to solve SAT instances using quantum techniques and compare it with state-of-the heart classical heuristics employed annually in SAT competitions. In the second part of the thesis, we consider a few classically well known algorithms for derivative free optimization which are ubiquitously employed in engineering problems. We propose a quantum speedup to this classical algorithm by using techniques of the quantum minimum finding algorithm. In the third part of the thesis, we consider practical applications in the fields of bio-informatics, petroleum refineries and civil engineering which involve solving either satisfiability or derivative free optimization. We investigate if using known quantum techniques to speedup these algorithms directly translate to the benefit of industries which invest in technology to solve these problems. In the last section, we propose a few open problems which we feel are immediate hurdles, either from an algorithmic or architecture perspective to getting a convincing speedup for the practical problems considered.

Thesis (M.Sc.)--Victoria University of Wellington, 2007. / Includes bibliographical references.