Related papers: Can Turnover Go to Zero?
Microreversibility rules the fluctuations of the currents flowing across open systems in nonequilibrium (or equilibrium) steady states. As a consequence, the statistical cumulants of the currents and their response coefficients at arbitrary…
We introduce the notion of a restricted exchangeable partition of $\mathbb{N}$. We obtain integral representations, consider associated fragmentations, embeddings into continuum random trees and convergence to such limit trees. In…
The inverse square potential arises in a variety of different quantum phenomena, yet notoriously it must be handled with care: it suffers from pathologies rooted in the mathematical foundations of quantum mechanics. We show that its…
We consider a renewal process which models a cumulative shock model that fails when the accumulation of shocks up-crosses a certain threshold. The ratio limit properties of the probabilities of non-failure after n cumulative shocks are…
We consider a simplified model for optimizing a single-asset portfolio in the presence of transaction costs given a signal with a certain autocorrelation and cross-correlation structure. In our setup, the portfolio manager is given two…
We consider 2-player zero-sum stochastic games where each player controls his own state variable living in a compact metric space. The terminology comes from gambling problems where the state of a player represents its wealth in a casino.…
We derive scaling limits for integral functionals of It\^o processes with fast nonlinear mean-reversion speed. We show that in these limits, the fast mean-reverting process is "averaged out" by integrating against its invariant measure.…
In this paper we derive fundamental limitations on the levels of $H_2$ and $H_\infty{}$ performance that can be achieved when controlling lossless systems. The results are applied to the swing equation power system model, where it is shown…
What is the best market-neutral implementation of classical Equity Factors? Should one use the specific predictability of the short-leg to build a zero beta Long-Short portfolio, in spite of the specific costs associated to shorting, or is…
We present explicit formulas - that are also computer code - for 101 real-life quantitative trading alphas. Their average holding period approximately ranges 0.6-6.4 days. The average pair-wise correlation of these alphas is low, 15.9%. The…
We consider a linear consensus system with n agents that can switch between r different connectivity patterns. A natural question is which switching law yields the best (or worst) possible speed of convergence to consensus? We formulate…
Iterative numerical algorithms are typically equipped with a stopping criterion, where the iteration process is terminated when some error or misfit measure is deemed to be below a given tolerance. This is a useful setting for comparing…
The problem of estimation error in portfolio optimization is discussed, in the limit where the portfolio size N and the sample size T go to infinity such that their ratio is fixed. The estimation error strongly depends on the ratio N/T and…
We consider a fading point-to-point link with packets arriving randomly at rate $\lambda$ per slot to the transmitter queue. We assume that the transmitter can control the number of packets served in a slot by varying the transmit power for…
We study how the effects of quantum corrections lead to notions of irreversibility and clustering in quantum field theory. In particular, we consider the virtual ``charge" distribution generated by quantum corrections and adopt for it a…
We obtain a lower asymptotic bound on the decay rate of the probability of a portfolio's underperformance against a benchmark over a large time horizon. It is assumed that the prices of the securities are governed by geometric Brownian…
This paper describes the reachable set and resolves an optimal control problem for the scalar conservation laws with discontinuous flux. We give a necessary and sufficient criteria for the reachable set. A new backward resolution has been…
The effects of model parameter uncertainty on traffic flow control problems have recently drawn research attention. While the uncertainty in fundamental diagram related parameters has been investigated in the past, few articles have focused…
A continuous-path semimartingale market model with wealth processes discounted by a riskless asset is considered. The numeraire portfolio is the unique strictly positive wealth process that, when used as a benchmark to denominate all other…
For continuous-time Markov chains we prove that, depending on the notion of effective affinity $F$, the probability of an edge current to ever become negative is either $1$ if $F< 0$ else $\sim \exp - F$. The result generalizes a ``noria''…