In illiquid markets, option traders may have an incentive to increase their portfolio value by using their impact on the dynamics of the underlying. We provide a mathematical framework to construct optimal trading strategies under market impact in a multi-player framework by introducing...

A new class of stochastic variables, governed by a specific set of rules, is introduced. These rules force them to loose some properties usually assumed for this kind of variables. We demonstrate that stochastic processes driven by these random sources must be described using a probability...

Noise is widely regarded as a residual category—the unexplained variance in a linear model or the random disturbance of a predictable pattern. Accordingly, formal models often impose the simplifying assumption that the world is noise-free and social dynamics are deterministic. Where noise...