Stochastic Portfolio Theory: an Overview

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On the martingale property of certain local martingales (2009, methodology): “We are grateful to Peter Bank, Nicholas Bingham, Mark Davis, Yuri Kabanov, Ioannis Karatzas, Walter Schachermayer, and two anonymous referees for valuable suggestions.”
Finitely Additive Probabilities and the Fundamental Theorem of Asset Pricing (2009, unknown): “Major examples include the benchmark approach in financial modeling of [24], as well as the emergence of stochastic portfolio theory [10], a descriptive theory of financial markets.”
Systems of Brownian particles with asymmetric collisions (2012, background): “1 in [11] that the ordered processes in a system of Brownian particles interacting through their ranks are given by independent Brownian motions, which have constant drift and diffusion coëfficients and collide in a symmetric fashion; that is, each collision local time is split equally between the t”
Convergence rates for rank-based models with applications to portfolio theory (2011, methodology): “According to the definition in [18], the rank-based models are not diverse, i.”