相关论文: Optimal stopping of Hunt and L\'evy processes

First, we give a closed-form formula for first passage time of a reflected Brownian motion with drift. This modifies a formula by Perry et al (2004). Second, we show that the maximum before a fixed drawdown is exponentially distributed for…

Optimal transport (OT) distances are finding evermore applications in machine learning and computer vision, but their wide spread use in larger-scale problems is impeded by their high computational cost. In this work we develop a family of…

The Green's functions for the Laplace equation respectively satisfying the Dirichlet and Neumann boundary conditions on the upper side of an infinite plane with a circular hole are introduced and constructed. These functions enables…

We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to…

This paper presents a physics-informed machine learning approach for synthesizing optimal feedback control policy for infinite-horizon optimal control problems by solving the Hamilton-Jacobi-Bellman (HJB) partial differential equation(PDE).…

This article explores an optimal stopping problem for branching diffusion processes. It consists in looking for optimal stopping lines, a type of stopping time that maintains the branching structure of the processes under analysis. By using…

L\'evy stable (jump-type) processes are examples of intrinsically nonlocal random motions. This property becomes a serious obstacle if one attempts to model conditions under which a particular L\'evy process may be subject to physically…

This paper studies an infinite horizon optimal tracking portfolio problem using capital injection in incomplete market models. The benchmark process is modelled by a geometric Brownian motion with zero drift driven by some unhedgeable risk.…

Optimal stopping is the problem of deciding when to stop a stochastic system to obtain the greatest reward, arising in numerous application areas such as finance, healthcare and marketing. State-of-the-art methods for high-dimensional…

The paper studies a class of multidimensional optimal stopping problems with infinite horizon for linear switching diffusions. There are two main novelties in the optimal problems considered: the underlying stochastic process has…

We propose \textit{DeepMartingale}, a deep-learning framework for the dual formulation of discrete-monitoring optimal stopping problems under continuous-time models. Leveraging a martingale representation, our method implements a…

A new approach to solving two-point boundary value problems for a wave equation is developed. This new approach exploits the principle of stationary action to reformulate and solve such problems in the framework of optimal control. In…

We study Sinkhorn's algorithm for solving the entropically regularized optimal transport problem. Its iterate $\pi_{t}$ is shown to satisfy $H(\pi_{t}|\pi_{*})+H(\pi_{*}|\pi_{t})=O(t^{-1})$ where $H$ denotes relative entropy and $\pi_{*}$…

We consider a general class of high order weak approximation schemes for stochastic differential equations driven by L\'evy processes with infinite activity. These schemes combine a compound Poisson approximation for the jump part of the…

Fractional Brownian motion is a non-Markovian Gaussian process $X_t$, indexed by the Hurst exponent $H$. It generalises standard Brownian motion (corresponding to $H=1/2$). We study the probability distribution of the maximum $m$ of the…

Let $X$ be a $n$-dimensional Ornstein-Uhlenbeck process, solution of the S.D.E. $$\d X_t = AX_t \d t + \d B_t$$ where $A$ is a real $n\times n$ matrix and $B$ a L\'evy process without Gaussian part. We show that when $A$ is non-singular,…

This paper concerns a class of infinite horizon optimal control problems with state constraints. By extending the needle variation method to the infinite horizon case we obtain a complete set of necessary optimality conditions for a strong…

We develop a method to solve, theoretically and numerically, general optimal stopping problems. Our general setting allows for multiple exercise rights, i.e., optimal multiple stopping, for a robust evaluation that accounts for model…

Motivated by the entropic optimal transport problem in unbounded settings, we study versions of Hilbert's projective metric for spaces of integrable functions of bounded growth. These versions of Hilbert's metric originate from cones which…

For nonparametric regression with one-sided errors and a boundary curve model for Poisson point processes we consider the problem of efficient estimation for linear functionals. The minimax optimal rate is obtained by an unbiased estimation…