Asian Journal of Probability and Statistics

This paper studies the optimal investment plan for a pension scheme with refund of contributions, stochastic salary and affine interest rate model. A modified model which allows for refund of contributions to death members’ families is considered. In this model, the fund managers invest in a risk free (treasury) and two risky assets (stock and zero coupon bond) such that the price of the risky assets are modelled by geometric Brownian motions and the risk free interest rate is of affine structure. Using the game theoretic approach, an extended Hamilton Jacobi Bellman (HJB) equation which is a system of non linear PDE is established. Furthermore, the extended HJB equation is then solved by change of variable and variable separation technique to obtain explicit solutions of the optimal investment plan for the three assets using mean variance utility function. Finally, theoretical analyses of the impact of some sensitive parameters on the optimal investment plan are presented.

This present study has discussed the levels and trends of under-five mortality in sub-Sahara Africa. This study aims to estimate under-five mortality using Summary of Birth Histories (SBH) of currently married women which may provide valuable information for assessing the interventions and measures already in place to achieve Sustainable Development Goals (especially goal 3). The Trussell variant which is the modified version of the Brass model was adopted to derive under-five mortality from SBH of currently married women. The result shows that the index for under-five mortality ( ) implied by the north family of the Coale–Demeny model life tables ranges from 65.8 deaths per 1000 live births in Zambia (2018 ZDHS) to as high as 132.9 deaths per 1000 live births in Nigeria (2018 NDHS) respectively. The average estimate of under-five mortality for the countries is about 107.9 deaths per 1000 live births for currently married women and 108.4 deaths per 1000 live births for the entire women in the surveys. While the average probability of a newborn baby surviving to age 5 is about 0.8921 for currently married women that of the entire women is about 0.8915.

This paper aims at making Bayesian analysis on the shape parameter of the exponential inverse exponential distribution using informative and non-informative priors. Bayesian estimation was carried out through a Monte Carlo study under 10,000 replications. To assess the effects of the assumed prior distributions and loss function on the Bayesian estimators, the mean square error has been used as a criterion. Overall, simulation results indicate that Bayesian estimation under QLF outperforms the maximum likelihood estimation and Bayesian estimation under alternative loss functions irrespective of the nature of the prior and the sample size. Also, for large sample sizes, all methods perform equally well.

Aims/ Objectives: The paper seeks to investigate the dynamic relationship between drivers licensing, vehicle registration, motorbike registration and accidents.
Study Design: Cross-sectional study.
Place and Duration of Study: The secondary data was collated on a monthly basis on Accidents, Driver license, Motor Registration and Vehicle Registration that spanned 9 years from January 2010 to December 2018 from the Upper East Regional Oce of the Drivers Vehicle and License Authority.

Methodology: The data was analyzed using vector autoregression model to establish the dynamic relationship between the variables. The R and Eviews softwares were used in the analysis.
Results: The ndings revealed that in the short-run and long-run neither Driver license, Vehicle Registration, Motor Registration none Accidents cannot in uence much on each other but experienced their own shock. Findings further ascertain that Accidents can granger cause vehicle registration to change but the remaining variable have no much in uence on accidents.Although, accidents can granger cause vehicle registration to change, the remaining variables had no
in uence on accidents. The nding nally concluded that ARCH-LM test indicated that there was no ARCH eect present in the series implying that the Vector Autoregression model was appropriate to establish the dynamic relationship between the variables.

We deal with backward doubly stochastic differential equations (BDSDEs) with a weak monotonicity and general growth generators and a square integrable terminal datum. We show the existence and uniqueness of solutions. As application, we establish the existenceand uniqueness of Sobolev solutions to some semilinear stochastic partial differential equations (SPDEs) with a general growth and a weak monotonicity generators. By probabilistic solution, we mean a solution which is representable throughout a BDSDEs.