Generalized volatility-stabilized processes

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 particular, we express the solution in terms of time changed squared-Bessel processes, and discuss sufficient conditions under which one can show that this solution is unique in distribution (respectively, does not explode). Sufficient conditions for the existence of a strong solution are also provided. Moreover, we discuss the significance of these processes in the context of arbitrage relative to the market portfolio within the framework of Stochastic Portfolio Theory. Copyright Springer-Verlag Berlin Heidelberg 2014