Related papers: Ergodic robust maximization of asymptotic growth w…

Stochastic and soft optimal policies resulting from entropy-regularized Markov decision processes (ER-MDP) are desirable for exploration and imitation learning applications. Motivated by the fact that such policies are sensitive with…

We discuss martingales, detrending data, and the efficient market hypothesis for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). Beginning with x-independent drift coefficients R(t) we show that Martingale stochastic…

In this paper we study the asymptotic theory for quadratic variation of a harmonizable fractional $\al$-stable process. We show a law of large numbers with a non-ergodic limit and obtain weak convergence towards a L\'evy-driven Rosenblatt…

Economists often estimate economic models on data and use the point estimates as a stand-in for the truth when studying the model's implications for optimal decision-making. This practice ignores model ambiguity, exposes the decision…

We study the optimal investment and proportional reinsurance problem of an insurance company, whose investment preferences are described via a forward dynamic utility of exponential type in a stochastic factor model allowing for a possible…

This paper investigates the investment problem of constructing an optimal no-short sequential portfolio strategy in a market with a latent dependence structure between asset prices and partly unobservable side information, which is often…

We deal with an infinite horizon, infinite dimensional stochastic optimal control problem arising in the study of economic growth in time-space. Such problem has been the object of various papers in deterministic cases when the possible…

This paper is concerned with asymptotic behavior of a variety of functionals of increments of continuous semimartingales. Sampling times are assumed to follow a rather general discretization scheme. If an underlying semimartingale is…

We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic volatility and unknown stock appreciation rate. The volatility parameter is driven by an external economic factor modeled as a…

This article provides an introduction to the asymptotic analysis of covariance parameter estimation for Gaussian processes. Maximum likelihood estimation is considered. The aim of this introduction is to be accessible to a wide audience and…

The paper considers the problem of robust estimating a periodic function in a continuous time regression model with dependent disturbances given by a general square integrable semimartingale with unknown distribution. An example of such a…

Consider a stochastic nonlinear system controlled over a possibly noisy communication channel. An important problem is to characterize the largest class of channels for which there exist coding and control policies so that the closed-loop…

Rough stochastic volatility models have attracted a lot of attentions recently, in particular for the linear option pricing problem. In this paper, starting with power utilities, we propose to use a martingale distortion representation of…

We consider a multi-period stochastic control problem where the multivariate driving stochastic factor of the system has known marginal distributions but uncertain dependence structure. To solve the problem, we propose to implement the…

We consider a game-theoretic model of a market where investors compete for payoffs yielded by several assets. The main result consists in a proof of the existence and uniqueness of a strategy, called relative growth optimal, such that the…

We derive the explicit solutions to singular stochastic control problems of the monotone follower type with (a) an expected discounted criterion, (b) an expected ergodic criterion and (c) a pathwise ergodic criterion. These problems have…

Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…

The problem of robust utility maximization in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models…

Some problems in the theory and applications of stochastic processes can be reduced to solving integral equations. While explicit solutions for these equations are often elusive, valuable insights can be gained through their asymptotic…

For an affine two factor model, we study the asymptotic properties of the maximum likelihood and least squares estimators of some appearing parameters in the so-called subcritical (ergodic) case based on continuous time observations. We…