Callable Russian options and their optimal boundaries.
Compatibility between pricing rules and risk measures: The CCVaR.
Conditional distributions, exchangeable particle systems, and stochastic partial differential equations
Stochastic partial differential equations (SPDEs) whose solutions are probability-measure-valued processes are considered. Measure-valued processes of this type arise naturally as de Finetti measures of infinite exchangeable systems of particles and as the solutions for filtering problems. In particular, we consider a model of asset price determination by an infinite collection of competing traders. Each trader’s valuations of the assets are given by the solution of a stochastic differential equation,...
Consistent stable difference schemes for nonlinear Black-Scholes equations modelling option pricing with transaction costs
This paper deals with the numerical solution of nonlinear Black-Scholes equation modeling European vanilla call option pricing under transaction costs. Using an explicit finite difference scheme consistent with the partial differential equation valuation problem, a sufficient condition for the stability of the solution is given in terms of the stepsize discretization variables and the parameter measuring the transaction costs. This stability condition is linked to some properties of the numerical...