Exact solutions of transaction cost nonlinear models for illiquid markets

Nonlinear option pricing models for illiquid markets: scaling properties and explicit solutions

Several models for the pricing of derivative securities in illiquid markets are discussed. A typical type of nonlinear partial differential equations arising from these investigation is studied. The scaling properties of these equations are discussed. Explicit solutions for one of the models are obtained and studied.

Models of self-financing hedging strategies in illiquid markets: symmetry reductions and exact solutions

We study the general model of self-financing trading strategies in illiquid markets introduced by Schönbucher and Wilmott, 2000. A hedging strategy in the framework of this model satisfies a nonlinear partial differential equation (PDE) which contains some function g(a). This function is deep connected to an utility function. We describe the Lie symmetry algebra of this PDE and provide a comple...

Pricing Options in Illiquid Markets: Optimal Systems, Symmetry Reductions and Exact Solutions

We study a class of nonlinear pricing models which involves the feedback effect from the dynamic hedging strategies on the price of asset introduced by Sircar and Papanicolaou. We are first to study the case of a nonlinear demand function involved in the model. Using a Lie group analysis we investigate the symmetry properties of these nonlinear diffusion equations. We provide the optimal system...

Exact solutions of nonlinear interval Volterra integral equations

Exact and numerical solutions for nonlinear differential equation of Jeffrey-Hamel flow