The Black Scholes model of option pricing constitutes the cornerstone of contemporary valuation theory. However, the model presupposes the existence of several unrealistic assumptions including the lognormal distribution of stock market price processes. There, now, subsists abundant empirical evidence that this is not the case. Consequently, several generalisations of the basic model have been ...

We consider the infinite horizon optimal consumption-investment problem under the drawdown constraint, i.e. the wealth process never falls below a fixed fraction of its running maximum. We assume that the risky asset is driven by the constant coefficients Black and Scholes model. For a general class of utility functions, we provide the value function in explicit form, and we derive closed-form ...

We consider the infinite horizon optimal consumption-investment problem under the drawdown constraint, i.e. the wealth process never falls below a fixed fraction of its running maximum. We assume that the risky asset is driven by the constant coefficients Black and Scholes model. For a general class of utility functions, we provide the value function in explicit form, and we derive closed-form ...

Under the assumptions of the market of Black and Scholes, options are redundant since, through the classic Black-Scholes delta hedging argument, they can be replaced by an equivalent combination the risky asset underlying the option and a risk free asset. We show that options are not redundant when small proportional transaction costs of size ε are added to the model, which provides mathematica...

In this work, we apply He’s variotional iteration method for obtaining analytic solutions to nonlinear Black-Scholes equation with boundary conditions for European option pricing problem. The analytical solution of the equation is calculated in the form a convergent power series with easily computable components. The powerful VIM method is capable of handling both linear and non-linear equation...

Using the symmetry group that was found in [1] and further studied in [2], in this work we study the partial differential equation of the Black-Scholes model [3] and relate such symmetries with the Mellin transform to find the price of an european like investment option. We also consider the Black-Schoes-Merton equation in the non-linear case that models investments in which volatility is a fun...

Under certain assumptions on the dependence structure of the residual lives of the insureds (independent, positively/negatively associated), in this paper we establish some laws of large numbers for the convex upper bounds, derived by the technique of comonotonicity, of the present value function of a homogenous portfolio composed of the whole-life insurance policies. Keyword: Convex order, com...

We consider a pure endowment contract whose life contingent payout is linked to the performance of a risky stock or index. Because of the additional mortality risk, the market is incomplete; thus, a fundamental assumption of the Black-Scholes theory is violated. We price this contract via the principle of equivalent utility and demonstrate that, under the assumption of exponential utility, the ...

In the finance market, Black–Scholes equation is used to model price change of underlying fractal transmission system. Moreover, fractional differential equations recently are accepted by researchers that a powerful tool in studying geometry and dynamics. Fractional modeling various important situations or phenomena real world such as fluid flow, acoustics, electromagnetic, electrochemistry mat...