arXiv subjects

Martin Šmíd

Publications and source records attributed to Martin Šmíd.

4 recordsLinked to original sources

arXiv2025

Has Anything Changed? Tracking Long-Term Interpretational Preferences in Quantum Mechanics

As we approach the centennial anniversary of modern quantum mechanics this paper revisits the foundational debates through a new poll within the research community. Inspired by the survey by Schlosshauer, Kofler, and Zeilinger at the specialized 2011 Quantum Physics and the Nature of Reality conference, we expanded our recruitment to include a more representative sample of the broader community of physicists with the aim to reveal potential shifts in scientists' views and compare our findings with those from several previous polls. While quantum foundations still lack a consensus interpretation, our results indicate a persistent preference for the Copenhagen interpretation. This enduring support likely reflects both the educational emphasis on the Copenhagen interpretation and its pragmatic appeal in avoiding complex metaphysical questions and introducing new notions (e.g., other worlds or the pilot wave). Our findings thus underscore the relative stability of interpretational preferences over the past decades.

quant-ph↗

arXiv2022

Contractivity of Bellman Operator in Risk Averse Dynamic Programming with Infinite Horizon

The paper deals with a risk averse dynamic programming problem with infinite horizon. First, the required assumptions are formulated to have the problem well defined. Then the Bellman equation is derived, which may be also seen as a standalone reinforcement learning problem. The fact that the Bellman operator is contraction is proved, guaranteeing convergence of various solution algorithms used for dynamic programming as well as reinforcement learning problems, which we demonstrate on the value iteration algorithm.

math.OC↗

arXiv2018

Zero Intelligence Models of the Continuous Double Auction: Econometrics, Empirical Evidence and Generalization

In the paper, a statistical procedure for estimating the parameters of zero intelligence models by means of tick-by-tick quote (L1) data is proposed. A large class of existing zero intelligence models is reviewed. It is shown that all those models fail to describe the actual behavior of limit order books close to the ask price. A generalized model, accommodating the discrepancies found, is proposed and shown to give significant results for L1 data from three US electronic markets. It is also demonstrated that the generalized model preforms significantly better than the reviewed models.

stat.AP↗

arXiv2016

Estimation of Zero Intelligence Models by L1 Data

A unit volume zero intelligence (ZI) model is defined and the distribution of its L1 process is recursively described. Further, a generalized ZI (GZI) model allowing non-unit market orders, shifts of quotes and general in-spread events is proposed and a formula for the conditional distribution of its quotes is given, together with a formula for price impact. For both the models, MLE estimators are formulated and shown to be consistent and asymptotically normal. Consequently, the estimators are applied to data of six US stocks from nine electronic markets. It is found that more complex variants of the models, despite being significant, do not give considerably better predictions than their simple versions with constant intensities.

stat.AP↗