The incorporation of non-linear pattern of early ages has led to new research
directions on improving the existing stochastic mortalitymodel structure. Several authors
have outlined the importance of encompassing the full age range in dealing with longevity
risk exposure, by not ignoring the dependence between young and old ages. In this study,
we consider the two extensions of the Cairns, Blake and Dowd model that incorporate the
irregularity profile seen at the mortality of lower ages, which are the Plat, and the O’Hare
and Li models respectively. The models’ performances in terms of in-sample fitting and
out-sample forecasts were examined and compared. The results indicated that the O’Hare
and Li model performs better as compared to the Plat model.
Non-parametric modeling is a method which relies heavily on data and motivated by the smoothness properties in estimating a function which involves spline and non-spline approaches. Spline approach consists of regression spline and smoothing spline. Regression spline with Bayesian approach is considered in the first step of a two-step method in estimating the structural parameters for stochastic differential equation (SDE). The selection of knot and order of spline can be done heuristically based on the scatter plot. To overcome the subjective and tedious process of selecting the optimal knot and order of spline, an algorithm was proposed. A single optimal knot is selected out of all the points with exception of the first and the last data which gives the least value of Generalized Cross Validation (GCV) for each order of spline. The use is illustrated using observed data of opening share prices of Petronas Gas Bhd. The results showed that the Mean Square Errors (MSE) for stochastic model with parameters estimated using optimal knot for 1,000, 5,000 and 10,000 runs of Brownian motions are smaller than the SDE models with estimated parameters using knot selected heuristically. This verified the viability of the two-step method in the estimation of the drift and diffusion parameters of SDE with an improvement of a single knot selection.
Recently, oil refining industry is facing with lower profit margin due to un-
certainty. This causes oil refinery to include stochastic optimization in making a decision
to maximize the profit. In the past, deterministic linear programming approach is widely
used in oil refinery optimization problems. However, due to volatility and unpredictability
of oil prices in the past ten years, deterministic model might not be able to predict the
reality of the situation as it does not take into account the uncertainties thus, leads to
non-optimal solution. Therefore, this study will develop two-stage stochastic linear pro-
gramming for the midterm production planning of oil refinery to handle oil price volatility.
Geometric Brownian motion (GBM) is used to describe uncertainties in crude oil price,
petroleum product prices, and demand for petroleum products. This model generates the
future realization of the price and demands with scenario tree based on the statistical
specification of GBM using method of moment as input to the stochastic programming.
The model developed in this paper was tested for Malaysia oil refinery data. The result
of stochastic approach indicates that the model gives better prediction of profit margin.
The flow of water over an obstacle is a fundamental problem in fluid mechanics.
Transcritical flow means the wave phenomenon near the exact criticality. The transcriti-
cal flow cannot be handled by linear solutions as the energy is unable to propagate away
from the obstacle. Thus, it is important to carry out a study to identify suitable model
to analyse the transcritical flow. The aim of this study is to analyse the transcritical
flow over a bump as localized obstacles where the bump consequently generates upstream
and downstream flows. Nonlinear shallow water forced Korteweg-de Vries (fKdV) model
is used to analyse the flow over the bump. This theoretical model, containing forcing
functions represents bottom topography is considered as the simplified model to describe
water flows over a bump. The effect of water dispersion over the forcing region is in-
vestigated using the fKdV model. Homotopy Analysis Method (HAM) is used to solve
this theoretical fKdV model. The HAM solution which is chosen with a special choice
of }-value describes the physical flow of waves and the significance of dispersion over a
bump is elaborated.
The growing number of multi-population mortality models in the recent years signifies the mortality improvement in
developed countries. In this case, there exists a narrowing gap of sex-differential in life expectancy between populations;
hence multi-population mortality models are designed to assimilate the correlation between populations. The present
study considers two extensions of the single-population Lee-Carter model, namely the independent model and augmented
common factor model. The independent model incorporates the information between male and female separately
whereas the augmented common factor model incorporates the information between male and female simultaneously.
The methods are demonstrated in two perspectives: First is by applying them to Malaysian mortality data and second
is by comparing the significance of the methods to the annuity pricing. The performances of the two methods are then
compared in which has been found that the augmented common factor model is more superior in terms of historical fit,
forecast performance, and annuity pricing.
Riverbank filtration (RBF) system is a surface water technology that is based
on the natural treatment of filtration instead of the use of chemicals, to pre-treat sur-
face water and provides public water supplies. Hydraulic conductivity value is one of the
significant factors affecting the water quality in RBF systems. In this article, an analyti-
cal modelling is developed to investigate the effect of this parameter on one dimensional
contaminant transport in RBF system. The model is solved by using Green’s function
approach. The model is applied for the first RBF system conducted in Malaysia. Gener-
ally, the results show that increasing the hydraulic conductivity value lead to an increase
in contaminant concentration in pumping well area.
Stochastic differential equations play a prominent role in many application areas including finance, biology and epidemiology. By incorporating random elements to ordinary differential equation system, a system of stochastic differential equations (SDEs) arises. This leads to a more complex insight of the physical phenomena than their deterministic counterpart. However, most of the SDEs do not have an analytical solution where numerical method is the best way to resolve this problem. Recently, much work had been done in applying numerical methods for solving SDEs. A very general class of Stochastic Runge-Kutta, (SRK) had been studied and 2-stage SRK with order convergence of 1.0 and 4-stage SRK with order convergence of 1.5 were discussed. In this study, we compared the performance of Euler-Maruyama, 2-stage SRK and 4-stage SRK in approximating the strong solutions of stochastic logistic model which describe the cell growth of C. acetobutylicum P262. The MS-stability functions of these schemes were calculated and regions of MS-stability are given. We also perform the comparison for the performance of these methods based on their global errors.
In this paper, the uncontrolled environmental factors are perturbed into the growth rate deceleration factor of the Gompertzian deterministic model. The growth process under Gompertz’s law is considered, thus lead to stochastic differential equations of Gompertzian with time delay. The Gompertzian deterministic model has proven to fit well with the clinical data of cancerous growth, however the performance of stochastic model towards clinical data is yet to be confirmed. The prediction quality of stochastic model is evaluated by comparing the simulated results with the clinical data of cervical cancer growth. The parameter estimation of stochastic models is computed by using simulated maximum likelihood method. 4-stage stochastic Runge-Kutta is applied to simulate the solution of stochastic model. Low values of root mean-square error (RMSE) of Gompertzian model with random effect indicate good fits.