Related papers: Dynamic Mean-Variance Asset Allocation in General …
Markowitz laid the foundation of portfolio theory through the mean-variance optimization (MVO) framework. However, the effectiveness of MVO is contingent on the precise estimation of expected returns, variances, and covariances of asset…
In this paper, which is a continuation of the previously published discrete time paper we develop a theory for continuous time stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a…
Changes in market conditions present challenges for investors as they cause performance to deviate from the ranges predicted by long-term averages of means and covariances. The aim of conditional asset allocation strategies is to overcome…
We present a method for optimal control of systems governed by partial differential equations (PDEs) with uncertain parameter fields. We consider an objective function that involves the mean and variance of the control objective, leading to…
Designing model-free algorithms for distributionally robust reinforcement learning (DRRL) poses fundamental challenges. The robust Bellman operator is nonlinear in the transition kernel, which makes one-sample Bellman updates biased, while…
Monotone mean-variance (MMV) utility is the minimal modification of the classical Markowitz utility that respects rational ordering of investment opportunities. This paper provides, for the first time, a complete characterization of optimal…
This paper is devoted to proposing a new asymmetric risk-sensitive criterion involving different risk attitudes toward varying risk sources. The criterion can only be defined through the initial value of the minimal solutions of quadratic…
We provide closed-form market equilibrium formula consolidating informational imperfections and investors beliefs. Based on Merton's model, we characterize the equilibrium expected excess returns vector with incomplete information. We then…
This paper analyzes and explicitly solves a class of long-term average impulse control problems with a specific mean-field interaction. The underlying process is a general one-dimensional diffusion with appropriate boundary behavior. The…
We suggest a new approach to creation of general market equilibrium models involving economic agents with local and partial knowledge about the system and under different restrictions. The market equilibrium problem is then formulated as a…
This paper studies the problem of steering large-scale multi-agent stochastic linear systems between Gaussian distributions under probabilistic collision avoidance constraints. We introduce a family of \textit{distributed covariance…
In this paper, we study a mean-variance optimization problem in an infinite horizon discrete time discounted Markov decision process (MDP). The objective is to minimize the variance of system rewards with the constraint of mean performance.…
We present a novel data-driven distributionally robust Model Predictive Control formulation for unknown discrete-time linear time-invariant systems affected by unknown and possibly unbounded additive uncertainties. We use off-line collected…
We study a discrete-time portfolio selection problem with partial information and maxi\-mum drawdown constraint. Drift uncertainty in the multidimensional framework is modeled by a prior probability distribution. In this Bayesian framework,…
Portfolio optimization constitutes a cornerstone of risk management by quantifying the risk-return trade-off. Since it inherently depends on accurate parameter estimation under conditions of future uncertainty, the selection of appropriate…
We consider a stochastic control problem for a class of nonlinear kernels. More precisely, our problem of interest consists in the optimisation, over a set of possibly non-dominated probability measures, of solutions of backward stochastic…
One of the core problems in mean-field control and mean-field games is to solve the corresponding McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs). Most existing methods are tailored to special cases in which the…
This study presents contemporaneous modeling of asset return and price range within the framework of stochastic volatility with leverage. A new representation of the probability density function for the price range is provided, and its…
We address the challenge of quantifying Bayesian uncertainty and incorporating it in offline use cases of finite-state Markov Decision Processes (MDPs) with unknown dynamics. Our approach provides a principled method to disentangle…
We consider mean-field control problems in discrete time with discounted reward, infinite time horizon and compact state and action space. The existence of optimal policies is shown and the limiting mean-field problem is derived when the…