相关论文: Ergodic aspects of trading with threshold strategi…

We consider an optimal control problem with ergodic (long term average) reward for a McKean-Vlasov dynamics, where the coefficients of a controlled stochastic differential equation depend on the marginal law of the solution. Starting from…

Strong invariance principles describe the error term of a Brownian approximation of the partial sums of a stochastic process. While these strong approximation results have many applications, the results for continuous-time settings have…

We consider an exploration algorithm where at each step, a random number of items become active while related items get explored. Given an initial number of items $N$ growing to infinity and building on a strong homogeneity assumption, we…

This paper deals with the ergodicity and the existence of a strong law of large numbers for adaptive Markov Chain Monte Carlo. We show that a diminishing adaptation assumption together with a drift condition for positive recurrence is…

Empirical studies indicate the presence of multi-scales in the volatility of underlying assets: a fast-scale on the order of days and a slow-scale on the order of months. In our previous works, we have studied the portfolio optimization…

This article studies the convergence properties of trans-dimensional MCMC algorithms when the total number of models is finite. It is shown that, for reversible and some non-reversible trans-dimensional Markov chains, under mild conditions,…

We discuss some classical and recent results and open problems on the statistical behavior of ergodic sums above toral translations, and their applications to Diophantine approximations and to ergodic properties of systems related to…

In this work, we study a natural nonparametric estimator of the transition probability matrices of a finite controlled Markov chain. We consider an offline setting with a fixed dataset, collected using a so-called logging policy. We develop…

We construct a diffusion approximation of a repeated game in which agents make bets on outcomes of i.i.d. random vectors and their strategies are close to an asymptotically optimal strategy. This model can be interpreted as trading in an…

We investigate how price variations of a stock are transformed into profits and losses (P&Ls) of a trend following strategy. In the frame of a Gaussian model, we derive the probability distribution of P&Ls and analyze its moments (mean,…

We extend to Lipschitz continuous functionals either of the true paths or of the Euler scheme with decreasing step of a wide class of Brownian ergodic diffusions, the Central Limit Theorems formally established for their marginal empirical…

We study Atlas-type models of equity markets with local characteristics that depend on both name and rank, and in ways that induce a stable capital distribution. Ergodic properties and rankings of processes are examined with reference to…

Devising models of the limit order book that realistically reproduce the market response to exogenous trades is extremely challenging and fundamental in order to test trading strategies. We propose a novel explainable model for small tick…

In ergodic physical systems, time-averaged quantities converge (for large times) to their ensemble-averaged values. Large deviation theory describes rare events where these time averages differ significantly from the corresponding ensemble…

We study scaled trinomial models converging to the Black--Scholes model, and analyze exponential certainty-equivalent prices for path-dependent European options. As the number of trading dates $n$ tends to infinity and the risk aversion is…

Ergodic optimization is the study of problems relating to maximizing orbits, maximizing invariant measures and maximum ergodic averages. An orbit of a dynamical system is called f-maximizing if the time average of the real-valued function f…

We propose two algorithms for the solution of the optimal control of ergodic McKean-Vlasov dynamics. Both algorithms are based on approximations of the theoretical solutions by neural networks, the latter being characterized by their…

A one-dimensional confined Nonlinear Random Walk is a tuple of $N$ diffeomorphisms of the unit interval driven by a probabilistic Markov chain. For generic such walks, we obtain a geometric characterization of their ergodic stationary…

Although financial models violate ergodicity in general, observing the ergodic behavior in the markets is not rare. Policymakers and market participants control the market behavior in critical and emergency states, which leads to some…

This paper considers the problem of consumption and investment in a financial market within a continuous time stochastic economy. The investor exhibits a change in the discount rate. The investment opportunities are a stock and a riskless…