In this paper, we devote ourselves to the research of numerical methods for American option pricing problems under the Black-Scholes model. The optimal exercise boundary which satisfies a nonlinear Volterra integral equation is resolved by a high-order collocationmethod based on gradedmeshes. For the other spatial domain boundary, an artificial boundary condition is applied to the pricing probl...

The Bohm-Vigier stochastic model is assumed as a natural generalization of the Black-Scholes in stock market. behavioral factor market recognizes hidden sector Bohmian mechanics. A Fokker-Planck equation description for presented. We find familiar Boltzmann distribution stationary solution model. return transition market, which corresponds with time-dependent equation, obtained.

In this paper, we investigate an optimal investment and consumption problem for an investor who trades in a Black–Scholes financial market with stochastic coefficients driven by a non-Gaussian Ornstein–Uhlenbeck process. We assume that an agent makes investment and consumption decisions based on a power utility function. By applying the usual separation method in the variables, we are faced wit...

We will reveal an interesting convex duality relationship between (a) minimizing the probability of lifetime ruin when the rate of consumption is stochastic and when the individual can invest in a Black-Scholes financial market; (b) a controller-and-stopper problem: the controller controls the drift and volatility of a process in order to maximize a running reward based on that process, the sto...

The Black-Scholes (1973) option pricing model provides the foundation for the modern theory of options valuation. In actual applications, however, the model has certain well-known deficiencies. For example, when calibrated to accurately price at-the-money options the Black-Scholes (1973) model often misprices deep in-the-money and deep out-of-themoney options. This model-anomalous behavior give...

The Black-Scholes equation is a partial differential that can model the European call option price problem. This be of order natural numbers or fractional. aim this paper to find solution fractional equation. method used solutions these equations Natural decomposition method. Two numerical examples are presented in paper. results show effective and easy use solve

An option pricing formula is obtained, based on a stochastic model with statistical feedback. The fluctuations evolve according to a Tsallis distribution which fits empirical data for stock returns. A generalized form of the Black-Scholes partial differential equation is derived, parametrized by the Tsallis entropic index q. A martingale representation is found, which allows us to use concepts ...