Neural networks optimize stopping boundaries in financial instruments.
problem Optimizing stopping boundaries in financial instruments.
method Deep neural networks and empirical risk minimization for parameterizing stopping boundaries.
result Proved existence of stopping boundary under natural assumptions.
Study optimal transport on simplex boundary, proving transport map and potential regularity.
problem Regularity of transport map and potential on simplex boundary.
method Boundary regularity results for optimal transport maps, exploiting simplex symmetries.
result Regularity properties of transport map and its convex potential.
We present three models of stock price with time-dependent interest rate, dividend yield, and volatility, respectively, that allow for explicit forms of the optimal exercise boundary of the finite maturity American put option. The optimal exercise boundary satisfies the nonlinear integral equation of Volterra type. We …
The paper analyzes Variable Annuities with surrender charges, providing a pricing formula and optimal exercise boundary.
problem Analyzing Variable Annuities with surrender charges and early termination rights.
method Formulated as an optimal stopping problem with a discontinuous payoff, non-monotonic optimal stopping boundaries are proven continuous and regular.
result A rigorous pricing formula and optimal exercise boundary for surrender options are derived.
Study on stock trading model with uncertain market status, proving free boundaries and optimal strategies.
problem Optimal trading strategies in a stock market with uncertain market status.
method Free boundary problem, variational inequality system, degenerate operator, C^∞-smoothness.
result All four switching free boundaries are no-overlapping, monotonic, and C^∞-smooth, and their relative localities are completely determined.
Optimal $C^{1, rac{1}{2}}$-regularity for H-surfaces with free boundary.
problem Proving optimal regularity for H-surfaces with free boundary. method Analyzing H-surfaces with free boundary on a C2-manifold. result Optimal $C^{1, rac{1}{2}}$ regularity up to the boundary.
Optimal inequality for free boundary hypersurfaces in convex domains.
problem Proving an optimal Heintze-Karcher inequality for free boundary hypersurfaces.
method Analyzing anisotropic free boundary hypersurfaces in convex domains.
result Optimal Heintze-Karcher-type inequality achieved for anisotropic free boundary Wulff shapes.
We consider the classification problem and focus on nonlinear methods for classification on manifolds. For multivariate datasets lying on an embedded nonlinear Riemannian manifold within the higher-dimensional ambient space, we aim to acquire a classification boundary for the classes with labels, using the intrinsic me…
In this paper we study a utility maximization problem with both optimal control and optimal stopping in a finite time horizon. The value function can be characterized by a variational equation that involves a free boundary problem of a fully nonlinear partial differential equation. Using the dual control method, we der…
Study on regularity of optimal transport maps on convex domains with quadratic cost.
problem Regularity of optimal transport maps between convex domains with quadratic cost.
method Analysis of Cα-densities and C1,α boundary conditions, monotonicity formula for optimal transport maps. result Proves C1,1−ε-regularity for nondegenerate Cα-densities and C2,α-regularity for C1,α boundary. Paper proposes a new classifier for hyperbolic spaces using horospherical boundaries.
problem Optimization of large margin classifiers in hyperbolic spaces.
method Horospherical decision boundaries for geodesically convex optimization.
result Geodesically convex optimization leads to globally optimal solutions.
Study detects boundaries in unlabeled noisy images without labels.
problem Detecting boundaries in unlabeled noisy images without labels.
method Proposed a continuous hinge-type surrogate loss for boundary detection, combined with deep neural networks.
result Deep neural network achieves minimax-optimal boundary recovery rate under piecewise smooth boundary model.
We derive a new equation for the optimal investment boundary of a general irreversible investment problem under exponential Lévy uncertainty. The problem is set as an infinite time-horizon, two-dimensional degenerate singular stochastic control problem. In line with the results recently obtained in a diffusive setting,…
Investigates how trading boundaries change with transaction costs in portfolio selection.
problem Investigates how trading boundaries vary with transaction costs in portfolio selection.
method Analyzes Merton's problem with proportional transaction costs, showing monotonicity of trading boundaries.
result Cost-adjusted trading boundaries are monotone in transaction costs, with implications for the Merton line.
We use probabilistic methods to characterise time dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications we consider a payoff of immediate stopping of "put" type and the underlying dynamics follows a geometric Brownian motion. The op…
A make-your-mind-up option is an American derivative with delivery lags. We show that its put option can be decomposed as a European put and a new type of American-style derivative. The latter is an option for which the investor receives the Greek Theta of the corresponding European option as the running payoff, and de…
Study finds optimal retirement timing in uncertain wage scenarios.
problem Optimal retirement timing in presence of uncertain wages.
method Formulated as a free boundary problem in an incomplete market.
result Developed a method to determine optimal retirement timing.
The paper studies free boundary minimal surfaces with many boundaries and their convergence to closed minimal surfaces.
problem Sharp isoperimetric inequalities for Steklov eigenvalues on surfaces with many boundary components.
method Maximization of Steklov eigenvalues and convergence analysis of free boundary minimal surfaces.
result Free boundary minimal surfaces converge to closed minimal surfaces in the boundary sphere as the number of boundary components increases.
The paper analyzes optimal retirement timing considering age-dependent mortality risk.
problem Optimal retirement timing under age-dependent mortality risk.
method Formulated as a stochastic control and optimal stopping problem, transformed into a finite time horizon, three-dimensional degenerate optimal stopping problem.
result Existence of an optimal retirement boundary, characterized as a unique solution to a nonlinear integral equation.
Paper generalizes Minkowski inequality for umbilical hypersurfaces with free boundary.
problem Optimal weighted Minkowski inequality for umbilical hypersurfaces with free boundary.
method Generalization of Xia's result to free boundary case in space forms.
result Free boundary version of optimal weighted Minkowski inequality in space forms.
A new model corrects inhomogeneity in Optimal Transport with Boundary.
problem Inhomogeneity in UROT models for Optimal Transport with Boundary.
method Proposed a modified entropic regularization term to make UROT models homogeneous.
result Homogeneous UROT model preserves properties of standard UROT while correcting inhomogeneity.
Study finds optimal boundaries for hedging a perpetual American put option.
problem Hedging perpetual American put options using delta hedging is impractical.
method Considered a seller of a perpetual American put option with a single trade.
result Determined optimal trading boundaries and hedging strategy.
Numerical methods solve Steklov eigenvalue problems to generate free boundary minimal surfaces.
problem Generating free boundary minimal surfaces using Steklov eigenvalue problems.
method Maximizing Steklov eigenvalues over a class of metrics, using conformal uniformization and gradient-based optimization.
result Numerical solutions for free boundary minimal surfaces with various boundary components.
Mixup reduces the sample complexity of finding optimal decision boundaries for more separable data.
problem Finding optimal decision boundaries in separable data distributions.
method Mixup technique applied to binary linear classification problems.
result Mixup significantly reduces the sample complexity for more separable data.
Solves a general class of free boundary Monge-Ampère equations.
problem Optimal transport with degenerate densities and geometric problems.
method Analyzes a specific class of Monge-Ampère equations and their applications.
result Solves the equations for a general class, including applications to optimal transport and geometric problems.
The study finds the optimal metrics for free boundary minimal surfaces in spherical caps.
problem Optimizing metrics for free boundary minimal surfaces in spherical caps.
method Introducing functionals based on eigenvalues of Steklov-type problems and proving maximizers are induced by immersions.
result Maximizing metrics are induced by free boundary minimal immersions in geodesic balls of a round sphere.
GCAO improves clustering of high-dimensional data by grouping low-density boundary points.
problem Stability and accuracy of clustering in high-dimensional, non-uniform data.
method Group-level optimization with gravitational attraction and optimization.
result GCAO outperforms 11 clustering methods on multiple datasets.
Optimally regularizes boundaries in the Heisenberg group with prescribed curvature.
problem Optimizing boundaries with prescribed sub-Finsler mean curvature in the Heisenberg group.
method Analyzes critical sets of the prescribed mean curvature functional in the Heisenberg group.
result Characteristic curves of critical sets are C2-regular, optimal in the Heisenberg group. This paper examines a Markovian model for the optimal irreversible investment problem of a firm aiming at minimizing total expected costs of production. We model market uncertainty and the cost of investment per unit of production capacity as two independent one-dimensional regular diffusions, and we consider a general…
It is known that the decision to purchase an annuity may be associated to an optimal stopping problem. However, little is known about optimal strategies, if the mortality force is a generic function of time and if the `subjective' life expectancy of the investor differs from the `objective' one adopted by insurance com…
Optimizes maps with controlled distortion for geometric tasks.
problem Free-boundary diffeomorphism optimization in geometric modeling.
method Least-squares quasiconformal (LSQC) operator and Spectral Beltrami Network (SBN).
result LSQC minimizer well-posed under mild conditions, stable under mesh refinement.
Probabilistic proof of smooth boundaries in optimal stopping problems.
problem Continuous differentiability of time-dependent optimal boundaries in optimal stopping problems.
method Local probabilistic arguments for a wider range of conditions.
result First probabilistic proof of continuous differentiability under general conditions.
Study asymptotic behaviors of solutions near singular boundaries for the Yamabe problem.
problem Boundary behavior of the singular Yamabe problem near singular boundaries.
method Analysis of asymptotic behaviors and derivation of optimal estimates for background metrics.
result Solutions are well approximated by solutions in tangent cones at singular points.
A fast, accurate method for pricing American options with free boundaries.
problem Pricing American options with free boundaries efficiently and accurately.
method A sixth-order compact finite difference scheme with a dynamic staggered boundary scheme and 3(2) R-K Bogacki-Shampine time stepping.
result An efficient sixth-order compact scheme for pricing American options with free boundaries.
Optimal constants for isoperimetric inequalities involving Steklov eigenvalues on surfaces are determined.
problem Determining optimal constants for isoperimetric inequalities involving Steklov eigenvalues on surfaces.
method Analyzing Riemannian surfaces with boundary, considering both given topology and conformal class, and proving inequalities relating conformal invariants and eigenvalues.
result New examples of topological disks realizing optimal constants and inequalities relating conformal invariants of Steklov eigenvalues on surfaces and disks are provided.
This paper improves boundary regularity of harmonic maps in metric measure spaces.
problem Improving boundary regularity of harmonic maps in non-smooth spaces.
method Developed a Gauss-Green formula for RCD(K,N) spaces and applied it to harmonic maps. result Optimal boundary regularity of harmonic maps from RCD(K,N)-spaces to CAT(0)-spaces. Study optimal times to buy and sell stocks using support/resistance lines.
problem Optimal times to buy and sell stocks based on support and resistance lines.
method Mathematical model with probabilistic methods to solve optimal stopping problems.
result Best times to buy and sell stocks are determined by solving free boundary problems.
Equivalences are known between problems of singular stochastic control (SSC) with convex performance criteria and related questions of optimal stopping, see for example Karatzas and Shreve [SIAM J. Control Optim. 22 (1984)]. The aim of this paper is to investigate how far connections of this type generalise to a non co…
Solves optimal stopping for Gauss-Markov bridges using time-space transformation.
problem Optimal stopping problem of a Gauss-Markov bridge.
method Time-space transformation approach, Picard iteration algorithm.
result Lipschitz continuity of the optimal stopping boundary and its characterization.
Optimal geodesics connect boundary points in Teichmüller space.
problem Finding optimal geodesics between boundary points of Teichmüller space.
method Analyzing horofunctions and Teichmüller geodesics.
result There is a unique optimal geodesic connecting boundary points.
The paper finds the largest eigenvalue for a specific type of domain in hyperbolic space.
problem Finding the domain with the largest first eigenvalue for a given volume and boundary conditions.
method Shape optimization for the first eigenvalue of the p-Laplace operator in hyperbolic space.
result The concentric annular region maximizes the first eigenvalue among multiply-connected domains.
Local conditions on boundaries of C∞ Levi-flat hypersurfaces, in case the boundary is a generic submanifold, are studied. For nontrivial real analytic boundaries we get an extension and uniqueness result, which forces the hypersurface to be real analytic. This allows us to classify all real analytic generic bou…
The study finds conditions for free boundary Hamiltonian stationary discs in complex 2-space.
problem Conditions for free boundary Hamiltonian stationary Lagrangian discs in complex 2-space.
method Established conditions for weakly conformal, branched Ω-free boundary Hamiltonian stationary Lagrangian immersions of discs. result If conditions are met, a disc is a free boundary minimal immersion.
Proves solutions to elliptic equations on Hermitian manifolds with optimal conditions.
problem Solving elliptic equations on Hermitian manifolds with boundary conditions.
method Derives quantitative boundary estimates and proves existence of solutions.
result Proves existence of solutions under almost optimal structural conditions.
We characterise the value function of the optimal dividend problem with a finite time horizon as the unique classical solution of a suitable Hamilton-Jacobi-Bellman equation. The optimal dividend strategy is realised by a Skorokhod reflection of the fund's value at a time-dependent optimal boundary. Our results are obt…
A new method solves American put options with high accuracy and speed.
problem Solving American put options with high accuracy and speed.
method Adaptive fourth-order Runge-Kutta-Fehlberg method coupled with a fourth-order compact scheme.
result The method provides a more accurate solution and better performance in terms of computational speed.
This paper embeds surfaces in 3D spheres and balls with minimal area.
problem Embed surfaces with boundary in B3 as minimal surfaces. method Optimizing Laplace and Steklov eigenvalues with symmetry groups.
result Proves existence of minimal surfaces in B3 with area below 2π. Two optimization problems for Loewner energy curves and their symmetries.
problem Optimizing Jordan curves and positive curves on boundary spaces.
method Using conformal welding and Möbius transformations.
result Symmetries between boundary spaces and pleated planes.