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In this paper, we obtain a duality result for the exponential utility maximization problem where trading is subject to quadratic transaction costs and the investor is required to liquidate her position at the maturity date. As an…
This work investigates the finite-horizon optimal covariance steering problem for discrete-time linear systems subject to both additive and multiplicative uncertainties as well as state and input chance constraints. In particular, a…
We consider the task of learning to control a linear dynamical system under fixed quadratic costs, known as the Linear Quadratic Regulator (LQR) problem. While model-free approaches are often favorable in practice, thus far only model-based…
In this paper, we study the optimal control problem for steering the state covariance of a discrete-time linear stochastic system over a finite time horizon. First, we establish the existence and uniqueness of the optimal control law for a…
In the past couple of decades, non-quadratic convex penalties have reshaped signal processing and machine learning; in robust control, however, general convex costs break the Riccati and storage function structure that make the design…
We investigate the portfolio selection problem for an agent with rank-dependent utility in an incomplete financial market. For a constant-coefficient market and CRRA utilities, we characterize the deterministic strict equilibrium…
In this paper, we consider a discrete-time stochastic control problem with uncertain initial and target states. We first discuss the connection between optimal transport and stochastic control problems of this form. Next, we formulate a…
We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-marginal martingale optimal transport problem. We propose two…
We investigate pricing-hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, e.g. a family of European options, only statically. In the first part of the paper we…
Nested simulation concerns estimating functionals of a conditional expectation via simulation. In this paper, we propose a new method based on kernel ridge regression to exploit the smoothness of the conditional expectation as a function of…
We present a midpoint policy iteration algorithm to solve linear quadratic optimal control problems in both model-based and model-free settings. The algorithm is a variation of Newton's method, and we show that in the model-based setting it…
In this paper we consider the problem of minimizing a quadratic functional for a discrete-time linear stochastic system with multiplicative noise, on a standard probability space, in infinite time horizon. We show that the necessary and…
An iterative learning algorithm is presented for continuous-time linear-quadratic optimal control problems where the system is externally symmetric with unknown dynamics. Both finite-horizon and infinite-horizon problems are considered. It…
This paper studies the weighted Hardy inequalities on the discrete intervals with four different kinds of boundary conditions. The main result is the uniform expression of the basic estimate of the optimal constant with the corresponding…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
We consider a discrete-time incomplete multi-asset market model with continuous price jumps. For a wide class of contingent claims, including European basket call options, we compute the bounds of the interval containing the no-arbitrage…
This paper studies the problem of optimal investment with CRRA (constant, relative risk aversion) preferences, subject to dynamic risk constraints on trading strategies. The market model considered is continuous in time and incomplete. the…
In this paper, we propose a class of discrete-time approximation schemes for stochastic optimal control problems under the $G$-expectation framework. The proposed schemes are constructed recursively based on piecewise constant policy. We…
The present paper provides a study of high-dimensional statistical arbitrage that combines factor models with the tools from stochastic control, obtaining closed-form optimal strategies which are both interpretable and computationally…
We consider the discretized version of a (continuous-time) two-factor model introduced by Benth and coauthors for the electricity markets. For this model, the underlying is the exponent of a sum of independent random variables. We provide…