ஜர்னல் ஆஃப் அப்ளைடு & கம்ப்யூட்டேஷனல் கணிதம்

Three contents for the pricing of bond options on the arbitrage-free model with jump are included in this paper. The first uses a new technique to derive a Closed-Form Solution (CFS) for bond options on Hull and White (HW) model with jump. The second deals with the pricing of bond option for Heath-Jarrow-Morton (HJM) model based on jump, and the third simulates the proposed models by the Monte Carlo Simulation (MCS). We also analyze the values obtained by the CFS and MCS. There is a substantial difference between bond option prices which are obtained by the HW model with jump and the HJM model based on jump. For this, we use the well-known Mean Standard Error (MSE) and show that lower value of Precision (PCS) in the proposed models corresponds to sharper estimates. In particular, we confirm that the PCS for the HJM based on jump is lower than that for the HW model with jump. Through the empirical simulation of our method suggested, we obtain a better accurate estimation for the pricing of bond options.

In this paper, we investigate the combine effects of magnetic field on the MHD flow of a third grade fluid through inclined channel in the presence of a uniform magnetic field with the consideration of heat transfer. Three different problems, Couette flow, Poiseuille flow and Couette-Poiseuille flow have been analysed. The non-linear differential equations governing the flow and heat transfer are solved for the velocity and temperature profile by employing the regular perturbation technique and the results are presented graphically.

This paper deals with a capacitated, multi-objective and solid transportation problem with imprecise nature of resources, demands, capacity of conveyance and cost. Here transportation cost is inversely varying with the quantity-to be transported from source to destinations in addition with a fixed per unit cost and a small vehicle cost. The transportation problem has been formulated as a constrained fuzzy non-linear programming problem. Next it is transformed into an equivalent crisp multi-objective problem using fuzzy interval approximation and then solved by Interactive Fuzzy Programming Technique (IFPT) and Generalized Reduced Gradient (GRG) method. An illustrative numerical example is demonstrated to find the optimal solution of the proposed model.

An investigation is made for unsteady MHD thin film flow of a third grade fluid down an inclined plane with no slip boundary condition. The governing nonlinear partial differential equations involved are reduced to linear partial differential equations using regular perturbation method. The resulting equations were solved using method of separation of variable and eigen functions expansion. The solutions obtained were examined and discussed graphically. It is interesting to find that the variation of the velocity and temperature profile with the magnetic field parameter and gravitational parameter depends on time.

We construct and study a differential infectivity model with chronological and infection age. The application is done on hepatitis B in Cameroon. We prove the global stability of the disease free equilibrium when the basic reproduction ratio R0 is less than one and the existence and uniqueness of an endemic equilibrium when R0>1 .

In this work, the numerical study of a deterministic mathematical model of an SEIVR (Susceptible-Exposed- Infected-Vaccinated-Recovered) epidemic model among infants was carried out. This model incorporates a temporary immune recovery class which involves subsequent dose vaccination for the infants. Hypothetical values were chosen for the parameters to test the validity of the mathematical model. The parameter with the greatest impact on the model was computed using the eigenvalue elasticity and sensitivity analyses and it was found that the parameter of the rate at which the vaccine wanes in the infants (ω) has the greatest impact on the mathematical model.