Related papers: One-sided solutions for optimal stopping problems …
L\'evy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic…
We consider controlling the paths of a spectrally negative L\'evy process by two means: the subtraction of `taxes' when the process is at an all-time maximum, and the addition of `bailouts' which keep the value of the process above zero. We…
We study two-armed Levy bandits in continuous-time, which have one safe arm that yields a constant payoff s, and one risky arm that can be either of type High or Low; both types yield stochastic payoffs generated by a Levy process. 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…
Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…
We propose a new method for solving optimal stopping problems (such as American option pricing in finance) under minimal assumptions on the underlying stochastic process $X$. We consider classic and randomized stopping times represented by…
This paper solves a recursive optimal stopping problem with Poisson stopping constraints using the penalized backward stochastic differential equation (PBSDE) with jumps. Stopping in this problem is only allowed at Poisson random…
This paper studies the long-time behavior of optimal solutions for a class of linear-convex optimal control problems. We focus on a partial exponential turnpike property, established without imposing controllability or stabilizability…
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…
Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a…
We study pure exploration problems in which the set of correct answers is possibly infinite. For example, such problems arise when regressing a continuous function on the means of the bandit or when learning Nash equilibria by querying…
We consider a stochastic impulse control problem that is motivated by applications such as the optimal exploitation of a natural resource. In particular, we consider a stochastic system whose uncontrolled state dynamics are modelled by a…
In this paper, the solvability of the Inverse Optimal Control (IOC) problem based on two existing minimum principal methods, is analysed. The aim of this work is to answer the question regarding what kinds of trajectories, that is depending…
We consider the problem of learning control policies that optimize a reward function while satisfying constraints due to considerations of safety, fairness, or other costs. We propose a new algorithm, Projection-Based Constrained Policy…
We study the optimal stopping problem for a monotonous dynamic risk measure induced by a BSDE with jumps in the Markovian case. We show that the value function is a viscosity solution of an obstacle problem for a partial…
This paper studies the optimization of Markov decision processes (MDPs) from a risk-seeking perspective, where the risk is measured by conditional value-at-risk (CVaR). The objective is to find a policy that maximizes the long-run CVaR of…
In this paper we study simulation based optimization algorithms for solving discrete time optimal stopping problems. This type of algorithms became popular among practioneers working in the area of quantitative finance. Using large…
Evolutionary strategies have recently been shown to achieve competing levels of performance for complex optimization problems in reinforcement learning. In such problems, one often needs to optimize an objective function subject to a set of…
We develop a theory of optimal stopping problems under G-expectation framework. We first define a new kind of random times, called G-stopping times, which is suitable for this problem. For the discrete time case with finite horizon, the…
We study optimal multiple stopping of strong Markov processes with random refraction periods. The refraction periods are assumed to be exponentially distributed with a common rate and independent of the underlying dynamics. Our main tool is…