Global \(C^1\) regularity of the value function in optimal stopping problems

DOI10.1214/19-AAP1517zbMath1472.60073arXiv1812.04564OpenAlexW2978815251MaRDI QIDQ2657902

Tiziano De Angelis, Goran Peskir

Publication date: 18 March 2021

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.04564

zbMATH Keywords

free boundary problemsmooth fitoptimal stopping problemregularity of a boundary pointregularity of a stochastic flowregularity of the value functionstrong Markov/Feller process

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Applications of stochastic analysis (to PDEs, etc.) (60H30) Stopping times; optimal stopping problems; gambling theory (60G40) Second-order elliptic equations (35J15) Free boundary problems for PDEs (35R35) Second-order parabolic equations (35K10)

Related Items

An analytical study of participating policies with minimum rate guarantee and surrender option ⋮ Parallel search for information in continuous time -- optimal stopping and geometry of the PDE ⋮ Detecting the presence of a random drift in Brownian motion ⋮ On an irreversible investment problem with two-factor uncertainty ⋮ The disorder problem for diffusion processes with the \(\epsilon \)-linear and expected total miss criteria ⋮ Discounted optimal stopping problems in continuous hidden Markov models ⋮ A change of variable formula with applications to multi-dimensional optimal stopping problems ⋮ Optimal dividend payout under stochastic discounting ⋮ The American put with finite‐time maturity and stochastic interest rate ⋮ Two-Sided Singular Control of an Inventory with Unknown Demand Trend ⋮ Finite horizon sequential detection with exponential penalty for the delay ⋮ Optimal execution with multiplicative price impact and incomplete information on the return ⋮ A new integral equation for Brownian stopping problems with finite time horizon ⋮ Perpetual American options with asset-dependent discounting ⋮ Weak equilibria for time‐inconsistent control: With applications to investment‐withdrawal decisions ⋮ On the Continuity of Optimal Stopping Surfaces for Jump-Diffusions ⋮ An optimal sequential procedure for determining the drift of a Brownian motion among three values ⋮ Optimal reduction of public debt under partial observation of the economic growth ⋮ Optimal dividends with partial information and stopping of a degenerate reflecting diffusion ⋮ Optimal Hedging of a Perpetual American Put with a Single Trade ⋮ Optimal stopping games in models with various information flows ⋮ A Dynkin Game on Assets with Incomplete Information on the Return ⋮ Stopping spikes, continuation bays and other features of optimal stopping with finite-time horizon ⋮ Quickest real-time detection of a Brownian coordinate drift ⋮ Mean-field games of finite-fuel capacity expansion with singular controls

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On J. Schauder's method to solve elliptic differential equations
• Continuity of the optimal stopping boundary for two-dimensional diffusions
• Embedding laws in diffusions by functions of time
• Parabolic variational inequalities in one space dimension and smoothness of the free boundary
• The regularity of free boundaries in higher dimensions
• Optimal stopping of the maximum process: The maximality principle
• Sulproblema di Dirichlet per l'equazione del calore
• Elliptic partial differential equations of second order
• From optimal stopping boundaries to Rost's reversed barriers and the Skorokhod embedding
• The dividend problem with a finite horizon
• Wiener's criterion for the heat equation
• Über lineare elliptische Differentialgleichungen zweiter Ordnung
• Quickest detection problems for Bessel processes
• On the continuity of the time derivative of the solution to the parabolic obstacle problem with variable coefficients
• On stochastic processes whose trajectories have no discontinuities of the second kind
• Applications of Choquet simplexes to elliptic and parabolic boundary value problems
• A change-of-variable formula with local time on curves
• REGULARITY OF BOUNDARY POINTS IN THE DIRICHLET PROBLEM FOR THE HEAT EQUATION
• Regular points, transversal sets, and Dirichlet problem for standard processes
• Potential Theory of Lévy Processes
• Multiparameter Processes
• A Change-of-Variable Formula with Local Time on Surfaces
• On Regular Boundary Points for Markov Processes
• Semimartingales and Subharmonic Functions