This work considers cooperative advertising in a manufacturer-retailer supply chain. While the manufacturer is the Stackelberg leader, the retailer is the follower. Using Sethi model it models the dynamic effect of the manufacturer and retailer's advertising efforts on sale. It uses optimal control technique and stochastic differential game theory to obtain the players' advertising strategies and the long-run value of the awareness share. Further, it models the relationship between the payoffs of both players and the awareness share. The work shows that with the provision of subsidy the retail advertising effort increases while the manufacturer's advertising effort reduces. It further shows that the total channel payoff is higher for subsidised retail advertising. However, the subsidy can only be possible if the rate of growth of the manufacturer's payoff is twice higher than that of the retailer.

This paper examines the variational form of classical portfolio strategy and expected terminal wealth for a Pension Plan Member (PPM) in a Defined Contribution (DC) Pension scheme. The flows of contributions made by PPM are invested into a market that is characterized by a cash account and a stock. It was assumed that the growth rate of salary of PPM is a linear function of time. The present value of PPM’s future contribution process was obtained. The optimal portfolio processes with inter-temporal hedging terms that offset any shocks to the stochastic cash inflows were established. The expected value of PPM’s terminal wealth was obtained

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This paper presents the Mellin transform method for the valuation of some vanilla power options with non-dividend yield. This method is a powerful tool used in the valuation of options. We extend the Mellin transform method proposed by Panini R. and Srivastav R.P. [15] to derive the price of European and American power put options with non-dividend yield. We also derive the fundamental valuation formula known as the Black-Scholes model using the convolution property of the Mellin transform method. To provide a sufficient numerical analysis, we compare the results generated by the Mellin transform method for the valuation of American power put option for n = 1 which pays no dividend yield to two other numerical methods namely Crank Nicolson finite difference method [2] and binomial model [3] for options valuation against Black-Scholes analytical pricing formula [1]. The numerical experiment shows that the Mellin transform method is efficient, easy to implement, agree with the values of Black-Scholes [1], Crank Nicolson finite difference method [2] and binomial model [3]. Hence the Mellin transform method is a better alternative method compared to the Crank Nicolsion finite difference and binomial model for the valuation of some vanilla power options.

We formulated and analysed a mathematical model to explore the cointeraction between malaria and schistosomiasis. Qualitative and comprehensive mathematical techniques have been applied to analyse the model. The local stability of the disease-free and endemic equilibrium was analysed, respectively. However, the main theorem shows that if RMS<1, then the disease-free equilibrium is locally asymptotically stable and the phase will vanish out of the host and if RMS>1, a unique endemic equilibrium is also locally asymptotically stable and the disease persists at the endemic steady state. The impact of schistosomiasis and its treatment on malaria dynamics is also investigated. Numerical simulations using a set of reasonable parameter values show that the two epidemics coexist whenever their reproduction numbers exceed unity. Further, results of the full malaria-schistosomiasis model also suggest that an increase in the number of individuals infected with schistosomiasis in the presence of treatment results in a decrease in malaria cases. Sensitivity analysis was further carried out to investigate the influence of the model parameters on the transmission and spread of malaria-schistosomiasis coinfection. Numerical simulations were carried out to confirm our theoretical findings.