Stochastic di®erential equations (SDEs) are　central to much of modern finance theory and have been widely used to model the behaviour of key variables such as the　instantaneous short-term interest rate, asset prices, asset returns and their volatility.　The explanatory and/or predictive...

This paper gives a review of numerical methods for solving the BSDEs, especially, finite difference methods. For numerical methods of finite difference, we should divide them into three branches. Distributed method (or parallel method) should now become a hot topic. It is a key reason we present...

This study was motivated by the poor performance of the current models used in stock return forecasting and aimed to improve the accuracy of the existing models in forecasting future stock returns. The current literature largely assumes that the residual term used in the existing model is white...

We solve, by using a monotone and stable approximation, the fully nonlinear degenerate parabolic equation derived by Cheridito, Soner and Touzi [8] from the stochastic control problem of super-replicating a contingent claim under gamma constraints. We present some numerical results.

Many stochastic differential equations (SDEs) do not have readily available closed-form expressions for their transitional probability density functions (PDFs). As a result, a large number of competing estimation approaches have been proposed in order to obtain maximum-likelihood estimates of...

This paper focuses on an econometric model which allows discontinuous change in an explained variable for a small continuous change in parameters. This model, given by stochastic differential equation with cubic drift, is called the cusp within standard catastrophe theory. The closed-form...

We study the convergence of Monte Carlo estimators of derivatives when the transition density of the underlying state variables is unknown. Three types of estimators are compared. These are respectively based on Malliavin derivatives, on the covariation with the driving Wiener process, and on...

This study was motivated by the poor performance of the current models used in stock return forecasting and aimed to improve the accuracy of the existing models in forecasting future stock returns. The current literature largely assumes that the residual term used in the existing model is white...