Sewe, S, Ngare P, Weke P.  2019.  Credit Scoring with Ego-Network Data. Journal of Mathematical Finance. 9(3):522-534. AbstractWebsite

This article investigates a stochastic filtering problem whereby the bor-rower’s hidden credit quality is estimated using ego-network signals. The hidden credit quality process is modeled as a mean reverting Ornstein-Ulehnbeck process. The lender observes the borrower’s behavior modeled as a continuous time diffusion process. The drift of the diffusion process is driven by the hidden credit quality. At discrete fixed times, the lender gets ego-network signals from the borrower and the borrower’s direct friends. The observation filtration thus contains continuous time borrower data augmented with discrete time ego-network signals. Combining the continuous time observation data and ego-network information, we derive filter equations for the hidden process and the properties of the conditional variance. Further, we study the asymptotic properties of the conditional variance when the frequency of arrival of ego-network signals is increased.


Jane Aduda1, Patrick Weke2, PN2.  2018.  A Co-Integration Analysis of the Interdependencies between Crude Oil and Distillate Fuel Prices. journal of mathematical finance. 8(2):478-496. AbstractA Co-Integration Analysis of the Interdependencies between Crude Oil and Distillate Fuel Prices

The co-evolution and co-movement of financial time series are of utmost importance in contemporary finance, especially when considering the joint behaviour of asset price realizations. The ability to model interdependencies and volatility spill-over effects introduces interesting dimensions in finance. This paper explores co-integrating relationships between crude oil and distillate fuel prices. Existence of multivariate co-integrating relations and bidirectional Granger-Causality is established among the series. It is also established that even after fitting a full VECM, the residuals are not necessarily multivariate normal suggesting the noise could as well be multivariate GARCH.


Lundengård, K, Ogutu C, Silvestrov S, Weke P.  2017.  Construction of moment-matching multinomial lattices using Vandermonde matrices and Gröbner bases. American Institute of Physics. (1):020094. Abstract

In order to describe and analyze the quantitative behavior of stochastic processes, such as
the process followed by a financial asset, various discretization methods are used. One such
set of methods are lattice models where a time interval is divided into equal time steps and
the rate of change for the process is restricted to a particular set of values in each time step.
The well-known binomial-and trinomial models are the most commonly used in applications,
although several kinds of higher order models have also been examined. Here we will
examine various ways of designing higher order lattice schemes with different node
placements in order to guarantee moment-matching with the process.


Weke, Patrick; Davis Bundi Ntwiga and Kirumbu, MK.  2016.  Trust Model for Social Network Using Singular Value Decomposition. Interdisciplinary Description of Complex Systems. 14(3):296-302. Abstract

For effective interactions to take place in a social network, trust is important. We model trust of agents using the peer to peer reputation ratings in the network that forms a real valued matrix.
Singular value decomposition discounts the reputation ratings to estimate the trust levels as trust is the subjective probability of future expectations based on current reputation ratings.
Reputation and trust are closely related and singular value decomposition can estimate trust using the real valued matrix of the reputation ratings of the agents in the network.
Singular value decomposition is an ideal technique in error elimination when estimating trust from reputation ratings. Reputation estimation of trust is optimal at the discounting of 20 %.

Weke, P, Ntwiga DB.  2016.  Credit Scoring for M-Shwari Using Hidden Markov Model. European Scientific Journal12. 12(15):176-188. Abstract

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.

Weke, P, Ntwiga DB, Manene M, Mwaniki I.  2016.  Trust and Distrust: A Reputation Ratings Approach. International Advanced Research Journal in Science, Engineering and Technology (IARJSET). 3(2):111-114. Abstract

Agents’ reputation ratings in a social network form a real valued matrix which is discounted with singular value decomposition (SVD) to estimate the trust and distrust levels of agents. SVD eliminates noise as future expected trust and distrust are based on current reputation ratings. A discounting of 20 percent is optimal, further discounting does not improve error reduction. Reputation and trust are closely related. Distrust is different from trust and reputation. Distrust is similar to trust negation; and trust is similar to distrust negation.

Weke, P, Ntwiga DB.  2016.  Consumer Lending Using Social Media Data. International Journal of Scientific Research and Innovative Technology. 3(2):1-8. Abstract

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.

Weke, P, Aduda J, Ngare P, Mwaniki IJ.  2016.  Financial Time Series Modelling of Trends and Patterns in the Energy Markets. Journal of Mathematical Finance. 6:324-337. Abstract

Energy use is behind virtually everything a person comes into contact with. The energy industry has rapidly expanded and become increasingly interdependent. In developed economies, the increase in energy consumption indicates a reliance on energy and its related products for continued and sustainable economic growth and development. Developing economies also rely on the development of energy resources to drive their growth. Energy was once viewed just as a utility, and an enabler with limited consumer interest, but now, it is key in the struggle for sustainable future economic growth [1] [2].
Energy prices, which are largely linked to oil prices, are a major concern for most economies. The recent financial crises and their ripple effects and after shocks have been largely unprecedented in terms of timing, speed and magnitude of impact on the world economies. Forecasting of crude oil prices is important for better investment and risk management and policy development, and econometric models are the most commonly used.

Ogutu, CA, Odweso GM.  2016.  BLUE, ABLE and Simplified Linear Estimation of the Selected Order Statistics from the Logistic Distribution. Far East Journal of Theoretical Statistics.


Njoora, D, Olubusoye OE.  2015.  Cross-Country Spillovers in East Africa: A Global Vector Autoregressive Analysis. American Journal of Theoretical and Applied Statistics. 4(3):125-137. Abstract

The recent financial crisis raises important issues about transmission of financial shocks across borders. This paper uses the global vector autoregressive model as developed in Dees, di Mauro, Pesaran and Smith (2007) to study cross- country interlinkages among East African countries. The paper uses trade weights to capture the importance of the foreign variables. Results reveal that there is no evidence of strong international linkages across countries in East Africa. Results also reveal that the variable in which a shock is simulated is the main channel through which-in the shortrun-shocks are transmitted, while the contribution of other variables becomes more important over longer horizons.

Sewe, SO, Mung'atu JK.  2015.  Modelling Time Varying Dependence of Financial Time Series: A Copula Approach. International Journal of Statistics and Economics. 16(1):1-15. Abstract

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.

Orowe, I, Ottieno J, Onyango N.  2015.  Multistate Modelling Vertical Transmission and Determination of R0 Using Transition Intensities. Applied Mathematical Sciences. 9(79):3941-3956. Abstract

In this paper multi-state modelling is used to determine the proba- bility distribution of the different states of vertical transmission of HIV. We start with a healthy-infected-dead three state model which we then modify and extend to a four state healthy-infected-treated-Aids four state model. Using the matrix approach we calculate their respection transition probabilities and compare the two models using the basic re- production number. In both models R0 < 1 suggesting that this mode of transmission will eventually be contained.


  2014.  Modelling Dependence Between the Equity and Foreign Exchange Markets Using Copulas. Applied Mathematical Sciences. 8(117):5813-5822. Abstract

Dependence between financial variables is a key consideration for portfolio diversification and risk management. Linear correlation as a measure of dependence is inadequate in capturing dependence of financial variables. In this paper we apply the semi parametric copula based multivariate dynamical model to estimate dependence structure between the equity and foreign exchange markets in Kenya. Several parametric copula models are fitted into the data and their performance in capturing the dependence compared. We find that there exists significant symmetric dependence between the variable. Besides, we find evidence of tail dependence amongst the variables. The findings of this paper are significant to global investors in their pursuit to diversify their portfolios and manage their risks.

Namugaya, J, Charles WM.  2014.  Modelling Stock Returns Volatility on Uganda Securities Exchange. Applied Mathematical Sciences. 8(104):5173-5184. Abstract

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.

Namugaya, J, Charles WM.  2014.  Modelling Volatility of Stock Returns: Is GARCH (1,1) Enough? International Journal of Sciences: Basic and Applied Research (IJSBAR). 16(2):216-223. Abstract

In this paper, we apply the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model of different lag order to model volatility of stock returns on Uganda Securities Exchange (USE). We use the Quasi Maximum Likelihood Estimation (QMLE) method to estimate the models. Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC) are used to select the best GARCH(p,q) model. From the empirical results, it has been found that USE returns are non-normal, positively skewed and stationary. Overall, GARCH(1,1) outperformed the other GARCH(p,q) models in modeling volatility of USE returns.

Silvestrov, K, Ogutu C, Silvestrov S, Weke P.  2014.  Asian Options, Jump-Diffusion Processes on a Lattice and Vandermonde Matrices. Modern Problems in Insurance Mathematics. , London: Springer Abstract

Modern Problems in Insurance Mathematics. Springer, London, Chapter 20, pages 337 – 366, XIX, 387 pages.
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].

Achia, TNO, Mwambi H, Weke P.  2014.  Statistical Properties of the Dorfman-Sterrett Group Screening Procedure with Errors in Decision. South African Statist. J.. 48(2014):1–18. Abstract

Methods that reduce the cost and time involved in detecting defective or nonconformal members of a large population have been explored extensively in the quality control literature.
These methods have also found extensive application in insect-vector, rodent-bacterium and blood screening. Group-screening designs are plans that identity defect factors in a large population by initially pooling factors together and then classifying each pool as nonconformal (NC) or conformal (C). Individual testing is then carried only amongst individual factors in pool that are found to be nonconformal. A modifications of this strategy, suggested by Sterrett (1957), proposes a reversion to a group test, in a group declared defective, upon detection of the first nonconformal factor and then carrying out individuals testing only if the new group is nonconformal. This procedure is referred to as the Dorfman-Sterrett procedure in the literature.
The statistical properties of the restricted Dorfman-Sterrett procedure, where the number of reversion to a group test is predetermined, has found little discussion in the literature. This study uses a testing of hypothesis approach to compare the performance of the Dorfman-Sterrett procedure with the Dorfman procedure assuming that factors or groups can be misclassified. Under the testing of hypothesis approach, using a 2g fractional factorial design, cost functions which are linear functions of expected total number of incorrect decisions and the expected.


Weke, P, Ratemo C.  2013.  Estimating IBNR Claims Reserves for General Insurance Using Archimedean Copulas. Applied Mathematical Sciences: Journal of Theory and Applications. 7(25):1223-1237.Website
Musiga, LA, Owino JO, Weke PGO.  2013.  Modeling a Hierarchical System with a Single Absorbing State.



Aduda, JA.  2011.  A Comparison of the Classical Black-Scholes Model and the GARCH Option Pricing Model for Currency Options. ICASTOR Journal of Mathematical Sciences. 5(2):267-284. Abstract

This paper looks at the consequences of introducing heteroscedasticity in option pricing. The analysis shows that introducing heteroscedasticity results in a better fitting of the empirical distribution of foreign exchange rates than in the Brownian model. In the Black-Scholes world the assumption is that the variance is constant, which is definitely not the case when looking at financial time series data. In this study, we therefore price a European call option under a GARCH Model Framework using the Locally Risk Neutral Valuation Relationship. Option prices for different spot prices are calculated using simulations. We use the non-linear in mean GARCH model in analyzing the Kenyan foreign exchange market.



O., PROFWEKEPATRICKGUGE.  2008.  A Comparison of the Classical Black-Scholes Model and the GARCH Option Pricing Model for Currency Options.. Proceedings of the 4th International Operations Research Society of Eastern Africa (ORSEA) Conference, October 23-24 August 2008, Nairobi, Kenya.. : ORSEA Abstract
Historia ya maisha binafsi kutoka kwale


O., PROFWEKEPATRICKGUGE.  2007.  Linear Estimation of Scale Parameter for Logistic Distribution Based on Consecutive Order Statistics.. Sankhya: The Indian Journal of Statistics Vol. 69 Part 4, pages 870 . : Sankhya: The Indian Journal of Statistics Abstract
Historia ya maisha binafsi kutoka kwale


Weke, PGO.  2006.  Optimal Portfolio with Risk Control.
O., PROFWEKEPATRICKGUGE.  2006.  Common Nearly Best Linear Estimates of Location and Scale Parameters: Normal and Logistic Distributions.. Far East J. of Theo. Stat. 18 (2), pp. 161 . 18(2):161-178.: Far East Journal of Theoretical Statistics AbstractWebsite

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O., PROFWEKEPATRICKGUGE.  2006.  The Bradley-Terry Model for Handling Categorical Response Variables from Farmer Participatory Trials.. Far East J. of Theo. Stat. . 20(2):163-178.: Far East Journal of Theoretical Statistics AbstractWebsite

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This paper looks at responses from participatory on-farm farmer participatory trials that are often measured as ratings (farmers score each given treatment on a scale that is ordered but arbitrary) or rankings (where farmers arrange the treatments in order from most preferred to least preferred). Simple methods such as the preference statistic that uses the proportion of responses, Kruskal-Wallis test which is a one-way analysis of variance by ranks and the Friedman test that is a two-way analysis of variance by ranks are outlined. The Bradley-Terry model for ranks which is a logit model for paired comparisons is described and used to fit models for plot level covariates.

O., PROFWEKEPATRICKGUGE.  2006.  Deterministic Claims Reserving in Short-Term Insurance Contracts.. E.A.J. of Statistics, Vol. 1, No. 2: 198 . : East African Journal of Statistics





Weke, PGO.  1992.  IBNR Claims Reserving and GLIM.

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