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...

Maximum drawdown is a risk measure that plays an important role in portfolio management. In this paper, we address the question of computing the expected value of the maximum drawdown using a partial differential equation (PDE) approach. First, we derive a two-dimensional convection-diffusion pricing equation for the maximum drawdown in the Black-Scholes framework. Due to the properties of the ...

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.

This paper deals with the numerical analysis of nonlinear Black-Scholes equation with transaction costs. An unconditionally stable and monotone splitting method, ensuring positive numerical solution and avoiding unstable oscillations, is proposed. This numerical method is based on the LOD-Backward Euler method which allows us to solve the discrete equation explicitly. The numerical results for ...

The purpose of this paper is to analyze and compute the early exercise boundary for a class of nonlinear Black–Scholes equations with a nonlinear volatility which can be a function of the second derivative of the option price itself. A motivation for studying the nonlinear Black–Scholes equation with a nonlinear volatility arises from option pricing models taking into account e.g. nontrivial tr...

In this paper we develop a high-order adaptive finite difference space-discretization for the Black–Scholes (B–S) equation. The final condition is discontinuous in the first derivative yielding that the effective rate of convergence is two, both for low-order and high-order standard finite difference (FD) schemes. To obtain a sixth-order scheme we use an extra grid in a limited spaceand time-do...

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