Insurance and Actuarial Sciencehttp://hdl.handle.net/2263/185982019-05-26T11:39:54Z2019-05-26T11:39:54ZEstimating age and the probability of being at least 18 years of age using third molars : a comparison between Black and White individuals living in South AfricaUys, AndreBernitz, HermanPretorius, SamanthaSteyn, M.http://hdl.handle.net/2263/652682018-08-27T09:54:46Z2018-09-01T00:00:00ZEstimating age and the probability of being at least 18 years of age using third molars : a comparison between Black and White individuals living in South Africa
Uys, Andre; Bernitz, Herman; Pretorius, Samantha; Steyn, M.
Third molar development of 705 White and 563 Black South African individuals aged between 15 and 25 years was assessed from panoramic radiographs obtained from the School of Dentistry, University of Pretoria, South Africa. The maxillary and mandibular left third molars were scored according to a ten-stage scoring system. Ancestry and sex differences in dental maturity were assessed, and the likelihood of an individual being 18 years of age was determined for each developmental stage. Statistically significant differences were noted among ancestry groups for most developmental stages, with South African Black individuals consistently maturing earlier than the White individuals. Statistically significant differences were noted among sex groups for some of the stages, mostly those near the final stages of root development. The results indicate that male third molars completed their development faster than that of females. The likelihood of an individual being 18 years of age based on the third molar development stage for the maxilla and mandible on its own was also determined. Combined likelihood results, for the maxillary and mandibular left third molars for stage H, increased the likelihood of being 18 years to 95% for all the studied ancestry and sex groups.
2018-09-01T00:00:00ZEstimating option-implied distributions in illiquid markets and implementing the Ross recovery theoremFlint, Emlyn JamesMare, Ebenhttp://hdl.handle.net/2263/643222018-03-29T01:05:46Z2017-01-01T00:00:00ZEstimating option-implied distributions in illiquid markets and implementing the Ross recovery theorem
Flint, Emlyn James; Mare, Eben
In this research we describe how forward-looking information on the statistical properties of an asset
can be extracted directly from options market data and demonstrate how this can be practically applied
to portfolio management. Although the extraction of a forward-looking risk-neutral distribution is
well-established in the literature, the issue of estimating distributions in an illiquid market is not. We
use the deterministic SVI volatility model to estimate weekly risk-neutral distribution surfaces. The
issue of calibration with sparse and noisy data is considered at length and a simple but robust fitting
algorithm is proposed. We further attempt to extract real-world implied information by implementing
the recovery theorem introduced by Ross (2015). Recovery is an ill-posed problem that requires careful
consideration. We describe a regularisation methodology for extracting real-world implied distributions
and implement this method on a history of SVI volatility surfaces. We analyse the first four moments
from the implied risk-neutral and real-world implied distributions and use them as signals within a
simple tactical asset allocation framework, finding promising results.
2017-01-01T00:00:00ZA method of parameterising a feed forward multi-layered perceptron artificial neural network, with reference to South African financial marketsSmith, M.L. (Mattie)Beyers, F.J.C. (Conrad)De Villiers, Johan Pieterhttp://hdl.handle.net/2263/602562017-05-09T01:02:27Z2016-01-01T00:00:00ZA method of parameterising a feed forward multi-layered perceptron artificial neural network, with reference to South African financial markets
Smith, M.L. (Mattie); Beyers, F.J.C. (Conrad); De Villiers, Johan Pieter
No analytic procedures currently exist for determining optimal artificial neural network structures and
parameters for any given application. Traditionally, when artificial neural networks have been applied
to financial modelling problems, structure and parameter choices are often made a priori without
sufficient consideration of the effect of such choices. A key aim of this study is to develop a general
method that could be used to construct artificial neural networks by exploring the model structure and
parameter space so that informed decisions could be made relating to the model design. In this study,
a formal approach is followed to determine suitable structures and parameters for a Feed Forward
Multi-layered Perceptron artificial neural network with a Resilient Propagation learning algorithm with
a single hidden layer. This approach is demonstrated through the modelling of four South African
economic variables, namely the average monthly returns on the money, bond and equity markets as
well as monthly inflation. Artificial neural networks can be constructed on the aforementioned variables
in isolation or, jointly, in an integrated model. The performance of a range of more traditional time
series models is compared with that of the artificial neural network models. The results suggest that,
on a statistical level, artificial neural networks perform as well as time series models at forecasting the
returns for financial markets. Hybrid models, combining artificial neural networks with the time series
models, are constructed, trained and tested for the money market and for the rate of inflation. They
appear to add value to the time series models when forecasting inflation, but not for the money market.
2016-01-01T00:00:00ZHattendorff’s theorem and Thiele’s differential equation generalizedhttp://hdl.handle.net/2263/304762017-08-07T09:24:22Z2007-02-20T00:00:00ZHattendorff’s theorem and Thiele’s differential equation generalized
Hattendorff's theorem on the zero means and uncorrelatedness of losses in disjoint time periods on a life insurance policy is derived for payment streams, discount functions and time periods that are all stochastic. Thiele's differential equation, describing the development of life insurance policy reserves over the contract period, is derived for stochastic payment streams generated by point processes with intensities. The development follows that by Norberg. In pursuit of these aims, the basic properties of Lebesgue-Stieltjes integration are spelled out in detail. An axiomatic approach to the discounting of payment streams is presented, and a characterization in terms of the integral of a discount function is derived, again following the development by Norberg. The required concepts and tools from the theory of continuous time stochastic processes, in particular point processes, are surveyed.
Dissertation (MSc (Actuarial Science))--University of Pretoria, 2007.
2007-02-20T00:00:00Z