In this paper we model the value of a firm based on its current earnings and cash balances. The value is modelled on the assumption that earnings follow a mean-reverting process. The effect of advertising on earnings is modelled, and the condition for optimal advertising derived. The value of...

We derive a nonlinear parabolic partial differential equation for the value of portfolios of options in the presence of proportional transaction costs. This assumes a Leland world of transacting after each time interval, which is of fixed length. The equation reduces to the modified variance...

The subject matter of this paper concerns the natural price barriers that markets encounter. The ideas in this paper can be applied to any market: equity, commodity, currency or fixed income. It is common market experience that prices (or yields) exhibit resistance and support: at key levels...

In this article, we present a flexible approach to the valuation of Parisian and similar exotic options. The approach is based on the numerical solution of a fundamental partial differential equation and can easily accommodate variations like American early exercise features, different payoff...