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In financial mathematics, the procedure for finding the solutions of the Black-Scholes model defined in terms of Arithmetic Asian Option (AAO) is one of the most tasking issues when considering its corresponding analytical solutions. In this paper, such analytical solution of a continuous arithmetic Asian option is obtained through the application of a proposed semi-analytical approach known as Projected Differential transform Method (PDTM). The Asian option model in continuous arithmetic form witnesses the application of PDTM for the first time in literature (to the authors’ best of knowledge). The PDTM entails less computational work, even without neglecting the high level of accuracy. The obtained solution is in agreement with those in literature via other solution methods. In terms of recommendation, the proposed solution method will be of great interest for related versions or forms of Asian option pricing models (geometric) likewise other financial nonlinear differential models. [ABSTRACT FROM AUTHOR]

In this work, we obtain analytical solutions of the time-fractional Black-Scholes equation for European call option via a proposed relatively new semi-analytic technique hereby referred to as Projected Differential Transform Method (PDTM). This algorithmic technique is a modified version of the classical Differential Transformation Method (DTM). We demonstrate the efficiency and accuracy of the proposed technique by solving some illustrative problems. The results are obtained with ease and less computational work. No linearization or perturbation is required unlike other contemporary techniques. Thus, our results show that the work of Edeki et al. [42] is a particular case of this present work. This proposed technique is being reported for the first time in literature for solving time-fractional Black-Scholes equation. It is therefore recommended as an alternative technique for solving linear and nonlinear equations resulting from timefractional stochastic differential equations (TFSDEs) in financial mathematics, with particular attention to stock option valuation; and fractional equations in applied sciences. [ABSTRACT FROM AUTHOR]

In spite of local and international efforts to end the scourge of poliomyelitis in the world, the disease still exists around the world with new cases being detected in otherwise polio-free areas while the known endemic places of Asia and Sub-Saharan Africa are yet to be ridden of the epidemic. Knowing with accuracy whether the disease has finally ended in a population has always being a subject of interest to mathematicians, statisticians and epidemiologists. In this study, we have defined a conditional probability function xic(t) as the probability of zero transmission agents given that there are initially (i) symptomatic (ii) infectives and (iii) asymptomatic carriers. Using the properties of Poisson process, two backward equations were derived which were jointly solved numerically. With these numerical solutions, we were able to formulate a model for the two identified transmission agents of poliomyelitis. [ABSTRACT FROM AUTHOR]

Eradicating poliomyelitis has been a major health concern to stakeholders the world over. In this study, we have developed a pair of stochastic equations for the extinction probability functions in two types of human transmission agents namely: infectives (types 1) and carriers (type 2). By solving the equations, the result shows that with only one asymptomatic carrier in a population, eradication is possible when (β22 + β21_µ)2 > 4β22µ where βij is the Poisson rate at which type i transmission agent produces type j transmission agent and β is the mean infectious period of the asymptomatic carriers. [ABSTRACT FROM AUTHOR]

In this paper, a proposed computational method referred to as Projected Differential Transformation Method (PDTM) resulting from the modification of the classical Differential Transformation Method (DTM) is applied, for the first time, to the Black-Scholes Equation for European Option Valuation. The results obtained converge faster to their associated exact solution form; these easily computed results represent the analytical values of the associated European call options, and the same algorithm can be followed for European put options. It is shown that PDTM is more efficient, reliable and better than the classical DTM and other semi-analytical methods since less computational work is involved. Hence, it is strongly recommended for both linear and nonlinear stochastic differential equations (SDEs) encountered in financial mathematics. [ABSTRACT FROM AUTHOR]

This work investigates the effect of stochastic capital reserve on actuarial risk analysis. The formulated mathematical problem is a risk-reserve process of an insurance company whose ruin and survival probabilities are analyzed via the solutions of a derived integro-differential equation (IDE). We further study the interplay between the parameters governing the ruin and the survival probabilities regarding the risk-reserve model; thereby establish a relationship between the probabilities and the initial risk reserve in terms of the other parameters. [ABSTRACT FROM AUTHOR]