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Optimal stopping is a fundamental class of stochastic dynamic optimization problems with numerous applications in finance and operations management. We introduce a new approach for solving computationally-demanding stochastic optimal…

We propose a machine learning enhanced algorithm for solving the optimal landing problem. Using Pontryagin's minimum principle, we derive a two-point boundary value problem for the landing problem. The proposed algorithm uses deep learning…

We formulate and solve a variant of the quickest detection problem which features false negatives. A standard Brownian motion acquires a drift at an independent exponential random time which is not directly observable. Based on the…

The optimal execution problem has always been a continuously focused research issue, and many reinforcement learning (RL) algorithms have been studied. In this article, we consider the execution problem of targeting the volume weighted…

We propose an efficient algorithm for the optimal control problems (OCPs) of nonlinear switched systems that optimizes the control input and switching instants simultaneously for a given switching sequence. We consider the switching…

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…

In this paper, we present a Longstaff-Schwartz-type algorithm for optimal stopping time problems based on the Brownian motion filtration. The algorithm is based on Le\~ao, Ohashi and Russo and, in contrast to previous works, our methodology…

This paper establishes a stochastic maximum principle for optimal control problems governed by time-changed forward-backward stochastic differential equations with L\'evy noise. The system incorporates a random, non-decreasing operational…

This paper addresses reflected backward stochastic differential equations (RBSDE hereafter) that take the form of \begin{eqnarray*} \begin{cases} dY_t=f(t,Y_t, Z_t)d(t\wedge\tau)+Z_tdW_t^{\tau}+dM_t-dK_t,\quad Y_{\tau}=\xi, Y\geq…

Solutions of stochastic Volterra (integral) equations are not Markov processes, and therefore classical methods, like dynamic programming, cannot be used to study optimal control problems for such equations. However, we show that by using…

We study a finite-horizon stochastic control criterion for non-convex optimization in which Brownian exploration is balanced against a quadratic control cost. Rather than emphasizing the classical Hopf--Cole representation, we isolate the…

In a classical optimal stopping problem the aim is to maximize the expected value of a functional of a diffusion evaluated at a stopping time. This note considers optimal stopping problems beyond this paradigm. We study problems in which…

We consider the minimization over probability measures of the expected value of a random variable, regularized by relative entropy with respect to a given probability distribution. In the general setting we provide a complete…

In this article we consider an optimization problem of expected utility maximization of continuous-time trading in a financial market. This trading is constrained by a benchmark for a utility-based shortfall risk measure. The market…

In this paper we formulate and study an optimal switching problem under partial information. In our model the agent/manager/investor attempts to maximize the expected reward by switching between different states/investments. However, he is…

We consider the problem of learning the optimal policy for Markov decision processes with safety constraints. We formulate the problem in a reach-avoid setup. Our goal is to design online reinforcement learning algorithms that ensure safety…

Policy Iteration (PI) is a widely used family of algorithms to compute optimal policies for Markov Decision Problems (MDPs). We derive upper bounds on the running time of PI on Deterministic MDPs (DMDPs): the class of MDPs in which every…

We consider the problem of the optimal trading strategy in the presence of linear costs, and with a strict cap on the allowed position in the market. Using Bellman's backward recursion method, we show that the optimal strategy is to switch…

We consider a two-way trading problem, where investors buy and sell a stock whose price moves within a certain range. Naturally they want to maximize their profit. Investors can perform up to $k$ trades, where each trade must involve the…

We investigate activities that have different periods of duration. We define the profit intensity as a measure of this economic category. The profit intensity in a repeated trading has a unique property of attaining its maximum at a fixed…