Abstract:
This work focuses on the optimization of investment contributions of pension asset with a view to improving contributors’ participation in achieving better return on investment (RoI) of their funds. We viewed some new regulations on Nigeria’s Contributory Pension Scheme” (CPS) from amended legislation of 2014, some of which are yet to be implemented when their regulations are approved. A mathematical model involving 5 variables, 5 inequality constraints covering regulatory limitations and limitation on scarce resource known as Asset Under Management (AUM), suggested and mathematically shown to be possible through “maximization of return irrespective of risk” while obeying all regulatory controls as our constraints optimized. Optimized portfolio using MatLab shows that the portfolio representing AES 2013 portfolio with a deficit growth of 15.75 m representing 3.27% less than the portfolio’s full growth potential within defined assumptions would have been averted if contributors actually set their targets and investment managers optimize from forecasts of future prices using trend analysis.

Abstract:
In this study, the research considered the application of the logistic distribution function to the assessment of risk of financial assets returns. The research first derived the distribution as a compound distribution of the Gumbel and Gamma distribution functions. The risk of financial assets returns data assessed.

Abstract:
Exchange rate is very pivotal in its role in the economy of any nation especially as a result of globalization. This paper seeks to model the Nigerian economy proxied by the log of Gross Domestic Product (LGDP) and its relationship with other variables in the economy. The variables used are NGN/USD exchange rate (NAIRA), log of oil revenue (LOILREV), log of government expenditure. We estimated the model using the Vector Autoregressive (VAR) model. We tested the presence or otherwise of causality among the variables using the method of Granger. The result reveals that the optimal lag for the model was 1. The exchange rate was found to Granger cause the economy (LGDP), LOILREV (Oil Revenue) and LGEXP (Government expenditure). We also discovered that the dynamics of NAIRA was not fully captured by the variables used. We also pointed out the shock persistence of NAIRA in time.

Abstract:
The problem of pricing contingent claims has beenextensively studied for non-Gaussian models, and in particular,Black- Scholes formula has been derived for the NIG assetpricing model. This approach was first developed in insurancepricing where the original distortion function was defined interms of the normal distribution.This approach was later studied to compare the standardBlack-Scholes contingent pricing and distortion basedcontingent pricing. In this paper, we aim at using distortionoperators by Cauchy distribution under a simpletransformation to price contingent claim. We also show that wecan recuperate the Black-Sholes formula using the distribution.

Abstract:
An earlier study proposed a stochastic algorithm based on a modified Robbins-Monroe type for the solution of finite-dimensional variational inequality problem. In this study we describe a similar approach for the linear complementarity problem. This study show that the stochastic algorithm arising from this approach converges strongly to the non-zero solution of the linear complementarity problem when it exists.

Abstract:
In this study, we investigate the effect of sudden increase in the income of individuals on the economy. Such situation arises in countries where upward adjustment of salaries increases the income of individuals by a certain percentage. We show that accumulated wealth of individuals through capital investment follows the power law distribution. We quantify the effect of low and high propensity, respectively, of an individual to invest on the economy using an empirical illustration.

Abstract:
This study tackled portfolio selection problem for an insurer as well as a
reinsurer aiming at maximizing the probability of survival of the Insurer and
the Reinsurer, to assess the impact of proportional reinsurance on the survival
of insurance companies as well as to determine the condition that would warrant
reinsurance according to the optimal reinsurance proportion chosen by the
insurer. It was assumed the insurer’s and the reinsurer’s surplus processes
were approximated by Brownian motion with drift and the insurer could purchase
proportional reinsurance from the reinsurer and their risk reserves followed
Brownian motion with drift. Obtained were Hamilton-Jacobi-Bellman (HJB)
equations which solutions gave the optimized values of the insurer’s and the
reinsurer’s optimal investments in the risky asset and the value of the
discount rate that would warrant reinsurance as a ratio of their portfolio weights
in the risky asset.

Abstract:
In this paper, optimal investment strategies for defined contribution (DC) Pension, with extra contribution are studied. Our model permits the plan member to make a defined extra contribution, as provided in the Nigerian Pension Reform Act of 2004. The plan member is free to invest in risk-free asset, and in two risky assets. A stochastic differential equation of the pension wealth that takes into account certain agreed proportions of the plan member’s salary, paid as contribution, and extra contribution towards the pension fund, is presented. The Hamilton-Jacobi-Bellman (H-J-B) equation, Legend transformation, and Dual theory are used to obtain the explicit solution of the optimal investment strategies for constant relative risk aversion (CRRA) utility function. We observed that the plan member will increase the proportion of his wealth to be invested in bond and stock and will reduce the proportion to be invested in cash.

Abstract:
In this paper, the optimal investment strategy for a defined contribution (DC) pension scheme was modeled with the assumption that the fund is invested partly in riskless assets and partly in risky assets. The market has a constant interest rate, a stochastic volatility that follows the Heston model, the salary is assumed constant over the entire career of the Pension Plan Participant (PPP) and the contribution is a constant proportion of the salary. The CRRA utility function was utilized to obtain a Hamilton-Jacobi-Bellman (HJB) equation. The resulting HJB equation was solved using the Prandtl Asymptotic Matching Method following the works in the literature.

Abstract:
This study examines a stochastic effect of the government policy on the income of individuals to explain the aggregate income of individuals whose salaries are increased and invested when received. A single (distribution) probability mass function which accommodates both the risk-free and risky income is presented herein. The result confirms that the aggregate income (wealth) of an individual is distributed according to power law. This distribution is used to solve the Black-scholes PDE. It is discovered that α (the measure exponent of the power law) lies between (1.2, 2.46) with the empirical data. We further used this distribution as a special (case) utility function to represent explicitly the optimal policies when there are minimum capital requirement.