Maximum likelihood estimation of discretely observed diffusion processes is mostly hampered by the lack of a closed form solution of the transient density. It has recently been argued that a most generic remedy to this problem is the numerical solution of the pertinent Fokker–Planck (FP) or...

We consider systems of interacting diffusion processes which generalize the volatility-stabilized market models introduced in Fernholz and Karatzas (Ann Finance 1(2):149–177, <CitationRef CitationID="CR5">2005</CitationRef>). We show how to construct a weak solution of the underlying system of stochastic differential equations. In...</citationref>

We provide simple, easy-to-test criteria for the existence of relative arbitrage in equity markets. These criteria postulate essentially that the excess growth rate of the market portfolio, a positive quantity that can be estimated or even computed from a given market structure, be...