The dynamics of commodity prices

In this paper we study the stochastic behavior of the prices and volatilities of a sample of six of the most important commodity markets and we compare these properties with those of the equity market. we observe a substantial degree of heterogeneity in the behavior of the series. Our findings show that it is inappropriate to treat different kinds of commodities as a single asset class as is frequently the case in the academic literature and in the industry. We demonstrate that commodities can be a useful diversifier of equity volatility as well as equity returns. Options pricing and hedging applications exemplify the economic impacts of the differences across commodities and between model specifications.

On the long time behavior of free stochastic Schrödinger evolutions

We discuss the time evolution of the wave function which is the solution of a stochastic Schrödinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations in space. We prove global existence and uniqueness of solutions. We observe that there exist three time regimes: the collapse regime, the classical regime and the diffusive regime. Concerning the latter, we assert that the general solution converges almost surely to a diffusing Gaussian wave function having a finite spread both in position as well as in momentum. This paper corrects and completes earlier works on this issue.