Prof. Joab O . Odhiambo, Ph.D.

This study explores a multiple-security, high-risk pricing model where the implied volatility has been portrayed through Generalized Wishart affine processes. The presence of dual dependency matrices distinctively characterizes this multifaceted model. These matrices encapsulate the relationship between the generalized Wishart processes and the evolving dynamics of several securities. The adaptability of the proposed model makes it a perfect fit for high-frequency market data, whether dealing with either long or short-term maturities of calls. The main objective paper is on its derivation and addressing the call option pricing problem within the context of the volatility mode using generalized Wishart stochastic. A combination of Fourier transforms techniques and perturbation methods are utilized, mainly focusing on pricing European call options. The model proposed in this study is theoretical and practical, showcasing the strong potential for real-world applications within the financial derivative market.

This research study proposes the inclusion of randomness or an error term in the modified Lee–Carter model, which improves the traditional Lee–Carter model for modeling and forecasting mortality risk for years in the actuarial science field. While the modified Lee–Carter model points out some of its common shortcomings , it has no distributional assumption that has been placed on the error/disturbance term. Incorporating a Gaussian distributional assumption on the error term is proposed, and then, the deep learning technique is used to obtain the parameter estimates. It is a departure from the traditional singular value decomposition estimation technique for estimating the parameters in the model. Finally, the Bühlmann credibility approach is incorporated into the model to determine its forecasting precision compared to the classical Lee–Carter model before applied in actuarial valuations.

Tis research study proposes the inclusion of randomness or an error term in the modifed Lee-Carter model, which improves the traditional Lee-Carter model for modeling and forecasting mortality risk for years in the actuarial science feld. While the modifed Lee-Carter model points out some of its common shortcomings , it has no distributional assumption that has been placed on the error/disturbance term. Incorporating a Gaussian distributional assumption on the error term is proposed, and then, the deep learning technique is used to obtain the parameter estimates. It is a departure from the traditional singular value decomposition estimation technique for estimating the parameters in the model. Finally, the Bühlmann credibility approach is incorporated into the model to determine its forecasting precision compared to the classical Lee-Carter model before being applied in actuarial valuations.

This study considered the modeling of systematic mortality risk for populations with finite data using the Poisson incorporated Credibility regression model. For novelty, we have included the credibility regression approach to modelling mortality by assuming the number of annual deaths follow a Poisson distribution. Our model shows improvement in precision levels when estimating mortality risk compared to classical models used in European countries. We have illustrated that our model works optimally when using Kenyan mortality data, comparing male and female lives under the different strategies, thus making better predictions than the classical Lee–Carter (LC) and Cairns–Blake–Dowd (CBD) models. The mean absolute forecast error (MAFE), mean absolute percentage forecast error (MAPFE), root mean square error (RMSE), and root mean square forecast error (RMSFE) under the incorporated credibility regression model are much lower than the values obtained without incorporation of the Buhlma...

is study considered the modeling of systematic mortality risk for populations with nite data using the Poisson incorporated Credibility regression model. For novelty, we have included the credibility regression approach to modelling mortality by assuming the number of annual deaths follow a Poisson distribution. Our model shows improvement in precision levels when estimating mortality risk compared to classical models used in European countries. We have illustrated that our model works optimally when using Kenyan mortality data, comparing male and female lives under the di erent strategies, thus making better predictions than the classical Lee-Carter (LC) and Cairns-Blake-Dowd (CBD) models. e mean absolute forecast error (MAFE), mean absolute percentage forecast error (MAPFE), root mean square error (RMSE), and root mean square forecast error (RMSFE) under the incorporated credibility regression model are much lower than the values obtained without incorporation of the Buhlmann credibility approach. e ndings of this research will help insurance companies, pension rms, and government agencies in sub-Saharan countries model and forecast systematic mortality risks accurately. Finally, the results are essential in actuarial modelling and pricing, thus making life assurance products a ordable for most people in low-income African countries.

Since the end of the Cold War, the dominant international strategy for promoting peace has been through the use of democracy. Proponents of democracy posit that democratic accountability lowers incentives for rebellion and conflict in general. This strategy is founded on the rationale that by making governments more accountable, then citizens would have less cause to resort to violence or opposition against the government. This argument is consistent with the liberal ideals espoused by democratic peace theorists that democracy tends to perpetuate peace. A system based on democratic values would guarantee justice, equality and liberty for the people and decrease the number of conflicts within the state. Kenya's transition to democracy is viewed in the same perspective; as an expansion of the political space to allow multiparty democracy to take root. Whilst political elections are a critical component to this process, events that occurred in the aftermath of Kenya's 2007 gene...

Many researchers who would wish to study Covid-19 may be wondering on which topic areas they should concentrate on even as the world grapples with this novel global pandemic. The following are some of the topic and research areas that a researcher can explore both during and post Covid-19 especially if you are a student or aspiring student looking for a topic which you would love to explore in your research. These are just some of the topics I thought would make great research areas and not limited as the world of research is massive. One can always do research in any area of study provided he or she has found a gap that needs to be filled through an extensive research.

Many actuarial science researchers on stochastic modeling and forecasting of systematic mortality risk use Cairns-Blake-Dowd (CBD) Model (2006) due to its ability to consider the cohort effects. A three-factor stochastic mortality model has three parameters that describe the mortality trends over time when dealing with future behaviors. This study aims to predict the trends of the model, kt(2) by applying the Recurrent Neural Networks within a Short-Term Long Memory (an artificial LSTM architecture) compared to traditional statistical ARIMA (p,d,q) models. The novel deep learning (machine learning) technique helps integrate the CBD model to enhance its accuracy and predictive capacity for future systematic mortality risk in countries with limited data availability, such as Kenya. The results show that Long Short-Term Memory network architecture had higher levels of precision when predicting the future systematic mortality risks than traditional methods. Ultimately, the results can b...

Since the inception of the novel Corona Virus Disease-19 in December in China, the spread has been massive leading World Health Organization to declare it a world pandemic. While epicenter of COVID-19 was Wuhan city in China mainland, Italy has been affected most due to the high number of recorded deaths as at 21st April, 2020 at the same time USA recording the highest number of virus reported cases. In addition, the spread has been experienced in many developing African countries including Kenya. The Kenyan government need to make necessary plans for those who have tested positive through self-quarantine beds at Mbagathi Hospital as a way of containing the spread of the virus. In addition, lack of a proper mathematical model that can be used to model and predict the spread of COVID-19 for adequate response security has been one of the main concerns for the government. Many mathematical models have been proposed for proper modeling and forecasting, but this paper will focus on using...

Since the outbreak of pandemic COVID-19 (Corona virus), many countries have continued to suffer economically leading to massive losses in terms of trillions of dollars globally in terms of trade loses. In reaction to this effect, many countries in the world have taken emergency measures to ensure that the impact does not lead to huge economic and financial implications in terms of rapid recession. In Africa, where many countries have taken measures to deal with global recession to the citizens especially through fiscal and monetary policies, which includes Kenya. In addition, the social economic statues have continued to change instantaneously and stochastically more so after huge number of populations losing their daily informal jobs with new measures to stop the spread of COVID-19 virus. This paper seeks to model the effect of COVID-19 pandemic on Kenyan Gross Domestic Product (GDP) contributors using a Discrete-time Markov Chain Analysis. In addition, the paper seeks to find the ...

The classical mortality models such as the Cairns-Blake-Dowd (CBD), Lee-Carter (LC), Linear Regression (LR) models are used to model Systematic Mortality Risk (SMR) for many developed countries populations for actuarial product valuations. This research study aims at incorporating the Bühlmann credibility approach (BCA) to improve the SMR models to fit sub-Saharan African populations like Kenya. Since the Kenyan population does not exhibit the Gaussian properties used in modeling the classical error terms, we proposed using Normal Inverse Gaussian distribution to model these error terms instead of a Gaussian distribution. We model the error terms of the classical models (LC, CBD, and LR) as a Normal Inverse Gaussian (NIG) distribution through the Bühlmann credibility approach. This novel approach demonstrates an improved precision of the predicted SMR as shown by the values of MAPE and RMSE measures compared to those under classical mortality risk models. Ultimately, we have done actuarial valuations of annuities and assurances using our determined SMR, thus concluding that this BCA approach improves the accuracy of actuarial products sold in the Kenyan market.

For a couple of years, many data scientists have been battling between Python & R programs especially on the levels of superiority. For any data scientist who would like build a machine or deep learning project, he or she may be stuck between selecting the right programming language when build it, you need to know that this article will help you make an informed decision. This article should elaborate the difference between these two commonly used languages in algorithms coding namely: Python and R; but also assist you know among the two languages, which has an upper edge over the other in a couple of ways. Ultimately, you will make a decision on which one to use when working on your project

In this decade, Data science seems to be the leading field of study because of the numerous opportunities it offers in terms business and financial solutions. Using Machine learning or deep learning approaches as a data scientist will leverage your skills above others thus making you competitive for the decade. In addition, the expertise in these areas puts you in a good position to secure a good job privately, publicly or as a consultant in respective areas. This paper should help you understand the opportunities that this decade brings in terms of research topics and areas for the data scientist or data analysts.

Since the outbreak of pandemic COVID-19 (Corona virus), many countries have continued to suffer economically leading to massive losses in terms of trillions of dollars globally in terms of trade loses. In reaction to this effect, many countries in the world have taken emergency measures to ensure that the impact does not lead to huge economic and financial implications in terms of rapid recession. In Africa, where many countries have taken measures to deal with global recession to the citizens especially through fiscal and monetary policies, which includes Kenya. In addition, the social economic statues have continued to change instantaneously and stochastically more so after huge number of populations losing their daily informal jobs with new measures to stop the spread of COVID-19 virus. This paper seeks to model the effect of COVID-19 pandemic on Kenyan Gross Domestic Product (GDP) contributors using a Discrete-time Markov Chain Analysis. In addition, the paper seeks to find the ultimate effect of the Covid-19 to the top five key sectors of the Kenyan economy that contributes massively to GDP growth by looking at the proportion of the contributors at steady state. Moreover, the results from this paper should help the government of Kenya as well as global investors to understand different economic stimulus planning packages to launch in the "hard-hit" sectors of the economy to reduce the impact of the potential economic recession. Ultimately, the information should be help in formulating a post COVID-19 economic recovery plan for the Kenyan economy but also act as a benchmark strategy for many other countries in Africa that has economic and financial dynamics similar to that of Kenya.

Many actuarial Science Students in Kenya often struggle to find research topics whenever they want to do their researches in the Universities. This Paper should give you an Overview of some of the best topics to choose when doing research at the end of the University course work.

Many researchers who would wish to study Covid-19 may be wondering on which topic areas they should concentrate on even as the world grapples with this novel global pandemic. The following are some of the topic and research areas that a researcher can explore both during and post Covid-19 especially if you are a student or aspiring student looking for a topic which you would love to explore in your research. These are just some of the topics I thought would make great research areas and not limited as the world of research is massive. One can always do research in any area of study provided he or she has found a gap that needs to be filled through an extensive research.

The Kenyan life insurance industry grew by 18.9% from 2017 to 2019. Ordinary life insurance, the class that comprises all Individual Life policies, is considered in this study. The cost of life insurance has been identified as a significant factor that affects the uptake of life insurance. The premium to charge is based on the actuarial present value of the sum assured. This value (per unit sum assured) is affected by the interest rate selected and the life table used to portray the uncertainty regarding the time until the death of the life insured. Kenyan life tables have been published twice (in 2007 and in 2015). The tables published in 2007 were developed using data whose quality was questionable in part because the period of study was too short. The tables published in 2015 are based on better quality data. However, the sample size is still relatively small. Parametric graduation and graduation with reference to a standard life table are two standard actuarial techniques used to produce life tables. Parametric graduation is the technique that is currently employed in developing the Kenyan life table. In this paper, graduation with reference to a standard life table is employed as an alternative. Additionally, the graduation parameters are estimated using the maximum likelihood technique as well as the more common weighted least squares estimation technique. The resulting life table is found to provide a better fit to the data with a lower degree of bias.