We consider a quasilinear parabolic equation with quadratic gradient terms. It arises in the modelling of an optimal portfolio which maximizes the expected utility from terminal wealth in incomplete markets consisting of risky assets and non-tradable state variables. The existence of solutions...

A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the...

We introduce and discuss a kinetic model for wealth distribution in a simple market economy which is built of a number of countries or social groups. Our approach is based on the model with risky investments introduced by Cordier, Pareschi and one of the authors in [13] and borrows ideas from...

Our goal is to identify the volatility function in Dupire's equation from given option prices. Following an optimal control approach in a Lagrangian framework, we propose a globalized sequential quadratic programming (SQP) algorithm with a modified Hessian - to ensure that every SQP step is a...

Based on a general specification of the asset speci?c pricing kernel, we develop a pricing model using an information process with stochastic volatility. We derive analytical asset and option pricing formulas. The asset prices in this rational expectations model exhibit crash-like, strong...

Kinetic equations modelling the redistribution of wealth in simple market economies is one of the major topics in the field of econophysics. We present a unifying approach to the qualitative study for a large variety of such models, which is based on a moment analysis in the related homogeneous...

Kinetic market models have been proposed recently to account for the redistribution of wealth in simple market economies. These models allow to develop a qualitative theory, which is based on methods borrowed from the kinetic theory of rarefied gases. The aim of these notes is to present a...

A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. In particular, the compact schemes of Rigal are generalized. The numerical results are compared to standard...

This paper analyzes the effect of non-constant elasticity of the pricing kernel on asset return characteristics in a rational expectations model. It is shown that declining elasticity of the pricing kernel can lead to predictability of asset returns and high and persistent volatility. Also,...

This paper presents a simple rational expectations model of intertemporal asset pricing. It shows that state-independent heterogeneous risk aversion of investors is likely to generate declining aggregate relative risk aversion. This leads to predictability of asset returns and high and...