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Model-free approaches for reinforcement learning (RL) and continuous control find policies based only on past states and rewards, without fitting a model of the system dynamics. They are appealing as they are general purpose and easy to…
This paper is concerned with a stochastic linear-quadratic optimal control problem with regime switching, random coefficients, and cone control constraint. The randomness of the coefficients comes from two aspects: the Brownian motion and…
This paper considers the problem of optimal liquidation of a position in a risky security in a financial market, where price evolution are risky and trades have an impact on price as well as uncertainty in the filling orders. The problem is…
In this paper, we discuss an application of the SDDP type algorithm to nested risk-averse formulations of Stochastic Optimal Control (SOC) problems. We propose a construction of a statistical upper bound for the optimal value of risk-averse…
Optimal control of heterogeneous mean-field stochastic differential equations with common noise has not been addressed in the literature. In this work, we initiate the study of such models. We formulate the problem within a linear-quadratic…
Foundation models often generate unreliable answers, while heuristic uncertainty estimators fail to fully distinguish correct from incorrect outputs, causing users to accept erroneous answers without any statistical guarantee. We address…
This paper studies the optimal output-feedback control of a linear time-invariant system where a stochastic event-based scheduler triggers the communication between the sensor and the controller. The primary goal of the use of this type of…
We consider a financial network represented at any time instance by a random liability graph which evolves over time. The agents connect through credit instruments borrowed from each other or through direct lending, and these create the…
This study develops an inverse portfolio optimization framework for recovering latent investor preferences including risk aversion, transaction cost sensitivity, and ESG orientation from observed portfolio allocations. Using controlled…
Through a stochastic control theoretic approach, we analyze reputation games where a strategic long-lived player acts in a sequential repeated game against a collection of short-lived players. The key assumption in our model is that the…
It is known that the implied volatility skew of FX options demonstrates a stochastic behavior which is called stochastic skew. In this paper we create stochastic skew by assuming the spot/instantaneous variance correlation to be stochastic.…
We study an optimal investment/consumption problem in a model capturing market and credit risk dependencies. Stochastic factors drive both the default intensity and the volatility of the stocks in the portfolio. We use the martingale…
We propose a stochastic game modelling the strategic interaction between market makers and traders of optimal execution type. For traders, the permanent price impact commonly attributed to them is replaced by quoting strategies implemented…
This paper focuses on optimal mismatched disturbance rejection control for linear continuoustime uncontrollable systems. Different from previous studies, by introducing a new quadratic performance index to transform the mismatched…
This paper is concerned with a linear-quadratic (LQ) leader-follower differential game with mixed deterministic and stochastic controls. In the game, the follower is a random controller which means that the follower can choose adapted…
We develop a dynamic trading strategy in the Linear Quadratic Regulator (LQR) framework. By including a price mean-reversion signal into the optimization program, in a trading environment where market impact is linear and stage costs are…
We investigated a cost-constrained static ergodic control problem of the variance of measure-valued affine processes and its application in streamflow management. The controlled system is a jump-driven mixed moving average process that…
This paper develops a unified explicit solution theory for optimal execution through sequential limit-order placement in a limit order book. Rather than controlling only the trading speed of a metaorder, we determine how individual limit…
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…
This paper mainly investigates reflected stochastic recursive control problems governed by jump-diffusion dynamics. The system's state evolution is described by a stochastic differential equation driven by both Brownian motion and Poisson…