PROF.WEKE PATRICK GUGE O

Aims: As shown in literature, several authors have adopted various individual frailty mixing distributions as a way of dealing with possible heterogeneity due to unobserved covariates in a group of insurers. This research contribution is to generalize the frailty mixing distribution to nest other classes of frailty distributions not in literature and apply the proposed distributions in valuation of life annuity business.

Methodology: A simulation study is done to assess the performance of the aforementioned models. The baseline parameters is estimated using Bayesian Inference and a better model is suggested for valuation of life annuity business.

Results: As a result of generalizing the frailty some new classes of frailty distributions are constructed such as; the Reciprocal Inverse Gaussian Frailty, the Inverse Gamma Frailty, the Harmonic Frailty and the Positive Hyperbolic Frailty.

From the simulation study, the proposed new frailty models shows that ignoring frailty leads to an underestimation of future residual lifetime since the survival curve shifts to the right when heterogeneity is accounted for. This is consistent with frailty literature.

The Reciprocal Inverse Gaussian model closely represents the Association of Kenya Insurers graduated rates with a slight increase in survival due to longevity risk.

Conclusion: The proposed new frailty models show an increase in the insurers expected liability when unobserved heterogeneity is accounted for. This is consistent with frailty literature and thus can be applied to avoid underestimating the insurer’s liability in the context of life annuity business.

The RIG model as proposed in estimating future liability by directly adjusting the AKI mortality rates shows an increase in longevity risk. The extent of heterogeneity of the insured group determines the level of risk. The RIG frailties should be considered for multivariate cases where the insureds are clustered in groups.

Nairobi Securities Exchange 20 Index Share (NSE-20 Share Index/ An Exchange Traded Fund) has been one of
the investment avenues for both Kenyans and foreign investors look whenever they want to make sound
investments decisions in the market. However, the assumption that the daily securities index prices follows a
normal distribution has been disputed by data in several cases. This means new statistical distributions must be
used to discern the distribution of NSE-20 Share Index thus enabling investors make prudent financial decisions
to avoid financial loses. In this research paper, we will model the prices of daily securities index using a log-normal
distribution. This is because the distribution follows a positive trend before we can ascertain on how well it fits
the already available data at the NSE market. This research paper recommends that a log-normal distribution best
fits data of the daily prices of NSE-20 Share Index for those investors who would like to model the future of the
market before making financial decisions.

Many businesses make profit yearly and tend to invest some of the profit so that they can cushion their organizations against any future unknown events that can affect their current profit making. Since future happenings in businesses cannot be predicted accurately, estimates are made using experience or past data which are not exact. The probability element (which is normally determined by experience or past data) is important in investment decision making process since it helps address the problem of uncertainty. Many of the investment decision making methods have incorporated the expectation and risk of an event in making investment decisions. Most of those that use risk account for diversifiable risk (non-systematic risk) only thus limiting the predictability element of these investment methods since total risk are not properly accounted for. A few of these methods include the certainty (probability) element. These include value at risk method which uses covariance matrices as total risk and the binning system which always assumes normal distribution and thus does not take care of discrete cases. Moreover comparison among various entities lacks since the probabilities derived are for individual entities and are just quantile values. Finite investment decision making using real market risk (non-diversifiable risk) was undertaken in this study. Non-diversifiable risk (systematic risk) estimates of a portfolio of stocks determined by a real risk weighted pricing model are used as initial data. The variance of non-diversifiable risk is estimated as a random variable referred to as random error (white noise). The estimator is used to calculate estimates of …

The introduction of mobile based Micro-credit facility, M-Shwari, has heightened the need to develop a proper decision support system to classify the customers based on their credit scores. This arises due to lack of proper information on the poor and unbanked as they are locked out of the formal banking sector. A classification technique, the hidden Markov model, is used. The poor customers’ scanty deposits and withdrawal dynamics in the M-Shwari account estimate the credit risk factors that are used in training and learning the hidden Markov model. The data is generated through simulation and customers categorized in terms of their credit scores and credit quality levels. The model classifies over 80 percent of the customers as having average and good credit quality level. This approach offers a simple and novice method to cater for the unbanked and poor with minimal or no financial history thus increasing financial inclusion in Kenya.

Consumer credit has been around for a long period of time but the dynamics observable from the consumers makes it hard to credit score and lend to the consumers. This difficulty results in the poor being excluded from receiving credit as they lack financial history. We analyze the limitations of the traditional consumer lending models due to use of historical data, and look at the benefits that could arise by incorporating social media data in credit scoring process for consumer lending. A review of the research progress made in using social media data for consumer scoring and lending process is presented. We found that social media data offers rich, vast and attractive information on changing trends and shifting demographics in credit underwriting of existing consumers and new consumers with minimal or no financial history. This data advances the lending process by widening the data set available and capture of new markets that are excluded from financial services.

Dependence between financial markets is a key concern for investors who seek to diversify their portfolios as they manage risks arising as a result of their investment decisions. In this paper we apply the copula theory to model dependence between the equity and the exchange rate markets of Kenya. We use the Semi Parametric Copula Based Multivariate Dynamical (SCOMDY) model proposed by (Chen and Fan, 2006) to estimate the dependence between these two markets. Using the moving window maximum likelihood estimation technique, we extend the SCOMDY estimator to capture time variation in the dependence. Our findings point to symmetric dependence in the markets. Amongst the parametric copula models fitted into the data, the t copula with 10 degrees of freedom is found to be the most appropriate for capturing the static dependence over the entire study period. Extreme value dependence is also present in the bivariate series whereby both markets rise and fall during periods of boom and bust. The hypothesis of homogeneity in dependence is rejected in all but three trading periods, pointing to the insufficiency of static parametric copula models to capture the dependence.

Stock returns volatility of daily closing prices of the Uganda Se- curities Exchange(USE) all share index over a period of 04/01/2005 to 18/12/2013 is Modelled. We employ different univariate Generalised Autoregressive Conditional Heteroscedastic(GARCH) models; both sym- metric and asymmetric. The models include; GARCH(1,1), GARCH-M, EGARCH(1,1) and TGARCH(1,1). Quasi Maximum Likelihood(QML) method was used to estimate the models and then the best performing model obtained using two model selection criteria; Akaike Information criterion(AIC) and Bayesian Information criterion(BIC). Overall, the GARCH(1,1) model outperformed the other competing models. This result is analogous with other studies, that GARCH(1, 1) is best.

Modern Problems in Insurance Mathematics. Springer, London, Chapter 20, pages 337 – 366, XIX, 387 pages.
Summary:
Risk is the uncertainty of an outcome and it can bring unexpected gains but can also cause unforeseen losses, even catastrophes. They are common and inherent in financial and commodity markets; for example; asset risk, interest rate risk, foreign exchange risk, credit risk, commodity risk. Investors have various attitudes towards risk, that is, risk aversion, risk seeking and risk neutral. Over the past few years financial derivatives have become increasingly important in the world of finance since they are kind of a risk management tool. A financial derivative is a financial instrument whose value depends on other fundamental financial assets, called underlying assets, such as stocks, indexes, currencies, commodities, bonds, mortgages and other derivatives (since we can have a derivative of a derivative). As an underlying asset one can also use a non-financial random phenomenon like for instance, weather conditions e.g. temperatures. Pricing derivatives accurately and quickly is important for risk management. This is important for both those who trade in derivatives and those who are willing to insure them. In this paper some lattice methods for pricing Asian options modeled using a jump diffusion process will be described. These methods can often be adapted to pricing of other derivatives or solving other types of problems in financial mathematics, for instance a jump diffusion process can be used to describe incoming claims to an insurance company, see [20].

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