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- ItemEstimating actuarial present value factors for annuity business using a non-parametric graduation approach(KNUST, 2019-06) Owusu, Derrick AsamoahAbstract Ensuring income security after retirement has been an issue troubling many countries. Over the years, several attempts have been made to improve upon pensions of retirees. A typical example is the introduction of the new pension scheme in Ghana. Yet, pensioners are still faced with the problem of nding an investment with a guaranteed payout for their pensions. To this end, the use of life annuities is proposed as a solution since life annuities have been touted to ensure a guaranteed payout. However, it is unfortunate to note that not only does Ghana lack a ready annuity market, the country also does not have a standard mortality table to undertake such annuity operations. Hence, in this study, the modi ed actuarial exposure method was applied to a pension scheme data in Ghana to estimate the crude mortality rates. The Whittaker-Henderson and the modi ed Whittaker-Henderson graduation methods were then applied to the estimated crude mortality rates to achieve a smooth and increasing progression of mortality rates with age. The Generalized Cross-Validation (GCV) method was then applied to obtain a suitable smoothing parameter, h at each order of di erencing, z that minimized the GCV score. The optimal set of graduated mortality rates with desirable features was produced by the Whittaker-Henderson method at z = 3 and h = 100. The selected graduated mortality rates were further used to compute life expectancy. Finally, annuity tables were developed from the estimated Actuarial Present Value (APV) factors to be used in pricing the annuity products.
- ItemSyntheses And Characterization Of Bismuth And Lead Chalcogenides And Their Ternary Alloys From Single Source Precursors(KNUST, 2018-07) Selina Ama SaahThis research describes the syntheses and characterization of lead and bismuth chalcogenide nanoparticles and thin films from single source precursors. The single source precursors used were dithiocarbonates, dithio- and diselenoureas, and dithiocarbamates. These precursors were characterized using micro-elemental analyses, thermogravimetric analyses, infrared spectroscopy, nuclear magnetic resonance spectrometry and mass spectrometry. The single crystal structures of bismuth ethyl xanthate and its 1, 10 phenanthroline adduct were determined. The complexes were used for the syntheses of nanoparticles using the hot injection and thin films using the spin coating technique. The as-synthesized nanoparticles and thin films were characterized by X-ray diffraction, scanning electron microscopy, transmission electron microscopy, inductively coupled plasma, energy dispersive X-ray spectroscopy and absorption measurements. Optical band gaps were estimated from the absorption data using Tauc’s plots. For the PbS thin films from lead dithiocarbonates, the effect of the alkyl chain length on the morphology and size of the nanocrystals were investigated. There was a change in morphology from cubes to fibrous structures as the alkyl chain changed from ethyl to dodecyl, thus confirming the anisotropic nature of PbS. SEM analyses of Bi2S3 thin films also showed a change in shape from nanowires of the bismuth ethyl xanthate to clusters of nanorods (triethylamine, pyridine) and nanodots (1,10 phenanthroline) depending on the choice of nitrogen adduct. Ternary PbSxSe(1-x) thin films deposited from lead xanthate and lead selenourea showed a gradual shift in p-XRD pattern to lower 2 theta values as the mole fraction of the lead selenourea complex in the coating mixture changed from 0 to 1 at an interval of 0.1. Estimated optical band gaps for the parent binaries (PbS and PbSe) and their ternary alloys (PbSxSe(1-x)) were all blue shifted from their respective bulk materials. PbSxSe(1-x) nanoparticles synthesized from lead thio- and selenourea complexes also exhibited a similar trend in both p-XRD and optical band gap. EDX analyses confirmed the presence of Pb, S and Se in all the PbSxSe(1-x) alloys formed at different atomic percentages depending on the ratios of the starting materials. The effects of different concentrations of Bi doping on the optical and structural properties of PbS nanoparticles have been investigated. Morphological studies showed cubes at 50% Bi doping suggesting the incorporation of the Bi atoms into the crystal lattice of the PbS nanoparticles. However, an interplay between rods and cubes were seen at 80% Bi doping. The estimated band gaps for PbS and Bi2S3 were 0.72 and 1.94 eV respectively with the alloy having band gaps in between the two binaries.
- ItemA Modal Approach To Price An Option In Continuous Time(KNUST, 2018) Osei AntwiAverage value options or Asian options have been priced using geometric and arithmetic averages of the underlying asset. However, these methods do not give accurate results especially in very low volatility regimes. In this study, we develop a new option pricing model based on the modal average of the underlying asset to price options. Using data from the NASDAQ in the United States of America we use the proposed model to price options sold on some stocks listed on the exchanges using software. The results consistently showed that for volatilities less than 3% of the underlying asset, the modal average option pricing model gives a better option price when compared to existing average option pricing models. Moreover, the modal average consistently does better at all levels of volatility when compared to the Black-Scholes model. We further proved analytically that the modal average model indeed does better than the geometric or arithmetic average models especially for low volatility stocks.
- ItemOn The Trapped Surface Characterization Of Black Hole Regions In The Spherically And Axially Symmetric Spacetimes(KNUST, 2018-04) Mohammed KumahThe characterization of black holes by means of classical event horizon is a global concept since one need to have the knowledge of the whole spacetime in order to locate a black hole region and the event horizon. To surmount these issues, we investigate alternative approach based on the concept of trapped surfaces in a variety of spacetimes. Specifically, to compute the expansions of the appropriate null vectors in both spherically and axiallysymmetric spacetimes and thus explicitly determine the existence of trapped and marginally trapped surfaces in their respective black hole regions
- ItemGreen Approach To Metal Chalcogenide Semiconductor Nanomaterials: Syntheses And Characterization Of Cds, Pbs, Zns, Mns And Mnxzn1-Xs Nanoparticles(KNUST, 2018-07) Micheal Baah MensahMetal chalcogenide nanomaterials such as CdS, PbS, ZnS, MnS and MnxZn1-xS are very useful compound semiconductors with potential applications in sensing, bioimaging, drug delivery, data storage and photovoltaic devices as well as in catalysis. However, the syntheses of good quality nanomaterials usually include toxic chemical reagents and therefore limit their application and adaptation to large scale production. Castor oil and single source precursors (SSPs) are suitable alternative green reagents for the syntheses of undoped and doped metal chalcogenide nanocrystals. In this thesis, green syntheses of (i) CdS nanoclusters and PbS nanorods/belts via thermal decomposition of xanthate complexes in castor oil, and (ii) ZnS, MnS and MnxZn1-xS nanocrystals via the thermal decomposition of diricinoleate carboxylate and heterocyclic dithiocarbamate complexes in oleylamine are reported. The dopant (Mn) feed concentration was varied in the range 0 ≤ x ≤ 0.1. The CdS displayed a band gap of 2.63 – 2.84 eV and a strong emission in the near-UV (λmax = 393 nm) region and formed small clusters of nanocrystals with average particle size of 6.78 1.89 nm. The PbS nanocrystals showed variety of morphologies. The average width and length of the PbS nanorods observed were 22.2 ( 2.3) nm and 225.9 ( 23.3) nm respectively. The activation energy obtained for the growth of ZnS nanoparticles in oleylamine was 53.41 kJ/mol. Powder-X-ray diffraction (p-XRD) patterns showed that the ZnS and MnxZn1-xS nanocrystals synthesized by different precursor routes were sphalerite and the shift in the lattice parameter indicated distortion due to the incorporation of the Mn(II) into the ZnS. The MnS nanocrystals were pure alabandite. The p-XRD patterns of the nanocrystals synthesized by the dithiocarbamate route showed some wurtzitic characteristics of ZnS and MnxZn1-xS. The band gap energy was found to decrease with increasing Mn(II) dopant concentration which indicated the introduction of trap states into the forbidden zone of the host ZnS. Luminescence was observed for MnxZn1-xS (for x ≤ 0.01) nanocrystals at 587 – 599.7 nm characteristic of Mn 4T16A1 transition suggesting possible incorporation of the Mn(II) into the ZnS host lattice. Electron paramagnetic resonance (EPR) studies confirmed the presence of Mn(II) ions dispersed at substitutionary sites for x ≤ 0.01 MnxZn1-xS nanocrystals. However, at high concentrations of Mn dopant (≥ 0.01), the Mn(II) ions were found bound to the surface/interstitial sites in ZnS. Thus, useful morphologies and interesting properties of important metal chalcogenide semiconductors were achieved by the use of environmentally benign materials.