A semigroup approach to generalized Black-Scholes type equations in incomplete markets

Game theoretic analysis of incomplete markets: emergence of probabilities, nonlinear and fractional Black-Scholes equations

Expanding the ideas of the author’s paper ’Nonexpansive maps and option pricing theory’ (Kibernetica, 34:6, 1998, 713-724) we develop a pure game-theoretic approach to option pricing, by-passing stochastic modeling. Risk neutral probabilities emerge automatically from the robust control evaluation. This approach seems to be especially appealing for incomplete markets encompassing extensive, so ...

On Nonlinear Black-Scholes Equations

This paper revisits some solution methods for Black-Scholes equation and some of its nonlinear versions arising in option pricing theory.

A new approach to using the cubic B-spline functions to solve the Black-Scholes equation

Nowadays, options are common financial derivatives. For this reason, by increase of applications for these financial derivatives, the problem of options pricing is one of the most important economic issues. With the development of stochastic models, the need for randomly computational methods caused the generation of a new field called financial engineering. In the financial engineering the pre...

Black Scholes the Martingale Approach

This paper establishes the Black Scholes formula in the martingale, risk-neutral valuation framework. The intent is two-fold. One, to serve as an introduction to expectation pricing and two, to examine this framework in explicit mathematical detail. The reader is assumed to have fluent background in the mathematical theory of stochastic processes and calculus, but is not assumed to have backgro...

The Black-Scholes-Merton Approach to Pricing Options