We derive a new equation for the optimal investment boundary of a general irreversible investment problem under exponential Lévy uncertainty. The problem is set as an infinite time-horizon, two-dimensional degenerate singular stochastic control problem. In line with the results recently...

In this paper, we show the existence of perfect hedging of options with liquidity risk when the stock price follows a geometric Brownian motion. For each option, there exist perfect hedging strategies for the party writing the option and the party buying the option. Partial differential...

This essay explores the link between the exponential probability density function and the present value function coupled with moment theory to derive important non probabilistic parameters from the Present value function in which are then used to derive a measure of the volatility of interest...