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We study a robust utility maximization problem in a general discrete-time frictionless market under quasi-sure no-arbitrage. The investor is assumed to have a random and concave utility function defined on the whole real-line. She also…
We give a singular control approach to the problem of minimizing an energy functional for measures with given total mass on a compact real interval, when energy is defined in terms of a completely monotone kernel. This problem occurs both…
In this paper, we develop a distributionally robust optimal control approach for differentially private dynamical systems, enabling a plant to securely outsource control computation to an untrusted remote server. We consider a plant that…
In control theory, typically a nominal model is assumed based on which an optimal control is designed and then applied to an actual (true) system. This gives rise to the problem of performance loss due to the mismatch between the true model…
Consider a storage system where the content is driven by a Brownian motion absent control. At any time, one may increase or decrease the content at a cost proportional to the amount of adjustment. A decrease of the content takes effect…
In this work, we investigate optimal control of a Brinkman equation couple with sixth-order Cahn-Hilliard equation. The Cahn-Hilliard equation is endowed with a source term accounting for mass exchange and the velocity equation contains a…
We consider a continuous time stochastic dynamic game between a stopper (Player $1$, the \textit{owner} of an asset yielding an income) and a controller (Player $2$, the \textit{manager} of the asset), where the manager is either effective…
This paper investigates the optimal control problem for a class of parabolic equations where the diffusion coefficient is influenced by a control function acting nonlocally. Specifically, we consider the optimization of a cost functional…
Conventional models of matching markets assume that monetary transfers can clear markets by compensating for utility differentials. However, empirical patterns show that such transfers often fail to close structural preference gaps. This…
We consider a problem of an optimal consumption strategy on the infinite time horizon when the short-rate is a diffusion process. General existence and uniqueness theorem is illustrated by the Vasicek and so-called invariant interval…
Aggregating risks from multiple sources can be complex and demanding, and decision makers usually adopt heuristics to simplify the evaluation process. This paper axiomatizes two closed related and yet different heuristics, narrow bracketing…
In this paper we study the single-item revenue management problem, with no information given about the demand trajectory over time. When the item is sold through accepting/rejecting different fare classes, Ball and Queyranne (2009) have…
We study the problem of optimal inside control of a stochastic Volterra equation driven by a Brownian motion and a Poisson random measure. We prove a sufficient and a necessary maximum principle for the optimal control when the trader has…
In this paper we study the optimization problem of an economic agent who chooses a job and the time of retirement as well as consumption and portfolio of assets. The agent is constrained in the ability to borrow against future income. We…
In this paper we investigate a utility maximization problem with drift uncertainty in a multivariate continuous-time Black-Scholes type financial market which may be incomplete. We impose a constraint on the admissible strategies that…
In stochastic control problems delicate issues arise when the controlled system can jump due to both exogenous shocks and endogenous controls. Here one has to specify what the controller knows when about the exogenous shocks and how and…
The need for control strategies that can address dynamic system uncertainty is becoming increasingly important. In this work, we propose a Model Predictive Control by quantifying the risk of failure in our system model. The proposed control…
The paper addresses an optimal control problem for a perturbed sweeping process of the rate-independent hysteresis type described by a controlled "play and stop" operator with separately controlled perturbations. This problem can be reduced…
This paper studies optimal consumption and saving decisions under uncertainty about the transition dynamics of the economic environment. We consider a general optimal savings problem in which the exogenous state governing discounting,…
Inventory and queueing systems are often designed by controlling weighted combination of some time-averaged performance metrics (like cumulative holding, shortage, server-utilization or congestion costs); but real-world constraints, like…