arXiv subjects

Matteo Ortisi

Publications and source records attributed to Matteo Ortisi.

3 recordsLinked to original sources

arXiv2013

From Minority Game to Black & Scholes pricing

In this paper we study the continuum time dynamics of a stock in a market where agents behavior is modeled by a Minority Game and a Grand Canonical Minority Game. The dynamics derived is a generalized geometric Brownian motion; from the Black & Scholes formula the calibration of both the Minority Game and the Grand Canonical Minority Game, by means of their characteristic parameters, is performed. We conclude that for both games the asymmetric phase with characteristic parameters close to critical ones is coherent with options implied volatility market.

q-fin.TR↗

arXiv2008

Polynomial rate convergence to an invariant measure for the continuum time limit of the Minority Game

In this paper we show that the continuum time version of the Minority Game satisfies the criteria for the application of a theorem on the existence of an invariant measure. We consider the special case of a game with "sufficiently" asymmetric initial condition where the number of possible choices for each individual is S=2 and $Γ<+\infty$. An upper bound for the asymptotic behavior, as the number of agents grows to infinity, of the waiting time for reaching the stationary state is then obtained.

math.PR↗

arXiv2007

A Law of Large Numbers for an Interacting Particle System with Confining Potential

In this paper we consider an interacting particle system modeled as a system of $N$ stochastic differential equations driven by Brownian motions with a drift term including a confining potential acting on each particle, and an interaction potential modeling the interaction among all the particles of the system. The limiting behavior as the size $N$ grows to infinity is achieved as a law of large numbers for the empirical process associated with the interacting particle system

math.PR↗