We establish existence, uniqueness and regularity of solution results for a class of backward stochastic partial differential equations with singular terminal condition. The equation describes the value function of non-Markovian stochastic optimal control problem in which the terminal state of the controlled process is…
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
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48 results for “singular terminal condition”
Study optimal trade execution in markets with price impact and resilience.
problem Optimal trade execution in illiquid markets with price impact and resilience.
method Modelled as a three-dimensional system of BSDEs with singular terminal condition, proving existence and uniqueness of solution.
result Characterized optimal strategy and value function in terms of BSDE solution.
We study a constrained optimal control problem with possibly degenerate coefficients arising in models of optimal portfolio liquidation under market impact. The coefficients can be random in which case the value function is described by a degenerate backward stochastic partial differential equation (BSPDE) with singula…
We provide a probabilistic solution of a not necessarily Markovian control problem with a state constraint by means of a Backward Stochastic Differential Equation (BSDE). The novelty of our solution approach is that the BSDE possesses a singular terminal condition. We prove that a solution of the BSDE exists, thus part…
Proves a sum limit for Kollár components in singularities.
problem Sum limit of -invariants in Kollár components.
method Analyzes Kawamata log terminal singularities.
result Sum of -invariants of two Kollár components is less than 1.
Proves finite step termination of Kähler-Einstein metric singularity formation.
problem Singularity formation of Kähler-Einstein metrics.
method Finite step termination of bubble trees for singularity formation.
result Finite step termination of Kähler-Einstein metric singularity formation proved in non-collapsing situation.
Paper finds unique viscosity solution to complex control problems.
problem Complex stochastic control problems with singular terminal state constraints.
method Establishes existence of unique nonnegative continuous viscosity solution using novel comparison principle.
result Unique viscosity solution to HJB equation for linear-quadratic control problems.
We introduce two simple models of forward-backward stochastic differential equations with a singular terminal condition and we explain how and why they appear naturally as models for the valuation of CO2 emission allowances. Single phase cap-and-trade schemes lead readily to terminal conditions given by indicator funct…
ETCNN uses neural networks to price American options accurately.
problem Accurately pricing American options with inequality constraints.
method ETCNN framework solving BSM equations with exact terminal condition.
result ETCNN achieves high accuracy and robustness across various scenarios.
Extends results on smoothability of singular Fano and Calabi-Yau varieties.
problem Smoothability of singular Fano and Calabi-Yau varieties under terminal singularities.
method Generalizes deformation theory results for Calabi-Yau and Fano threefolds to higher dimensions, using higher Du Bois and rational singularities.
result Identifies a class of singularities for which smoothing results hold, including generalized Fano and Calabi-Yau varieties.
Proves orbifold singularities for Ricci-flat metrics on certain Kähler varieties.
problem Regularity of singular Ricci-flat Kähler metrics on Kähler varieties with log terminal singularities.
method Analyzes orbifold singularities of metrics restricted to the orbifold locus.
result Singular Ricci-flat Kähler metrics on Kähler varieties with log terminal singularities have orbifold singularities.
Proof of complex geometry theorem for specific singular spaces.
problem Proving a complex geometry theorem for a specific type of singular spaces.
method Self-contained proof of singular Beauville-Bogomolov decomposition theorem.
result Proof of singular Beauville-Bogomolov decomposition theorem for compact Kähler varieties with log terminal singularities and zero first Chern class.
A System of BSDEs with Singular Terminal Values Arising in Optimal Liquidation with Regime Switchingq-fin.MF
Study optimal liquidation with multiple regimes using BSDEs with singular terminal values.
problem Optimal liquidation with regime switching in dark pools.
method Introduced a system of BSDEs with jumps and singular terminal values.
result Existence and uniqueness results for the BSDE system are obtained.
Researchers find Kähler-Einstein metrics near isolated log terminal singularities.
problem Existence of Kähler-Einstein metrics with positive curvature near isolated log terminal singularities.
method Solving complex Monge-Ampère equations to analyze the existence of metrics.
result Existence of smooth solutions in subcritical regimes, with critical exponent expressed in terms of normalized volume.
We study the existence of a minimal supersolution for backward stochastic differential equations when the terminal data can take the value + with positive probability. We deal with equations on a general filtered probability space and with generators satisfying a general monotonicity assumption. With this minim…
Proves finitely generated graded rings for klt singularities.
problem Understanding the structure of klt singularities.
method Analyzes graded rings associated with minimizers of normalized volume functions.
result Graded rings are finitely generated for klt singularities.
Constructs Kahler-Einstein metrics near isolated log canonical singularities.
problem Constructing metrics near singularities in complex geometry.
method Constructs Kahler-Einstein metrics with negative scalar curvature near isolated log canonical singularities.
result Metrics are complete near the singularity if the underlying space has complex dimension 2 or if the singularity is smoothable.
Study two types of singular Kähler-Einstein metrics on complex varieties.
problem Understanding different types of singular Kähler-Einstein metrics.
method Analyzing Ricci flat Kähler cone metrics and applying to more general spaces.
result A weaker notion of singular Kähler-Einstein metrics is equivalent to a stronger one under certain conditions.
Develops theory for Kähler-Ricci flow on singular varieties.
problem Analyzing Kähler-Ricci flow on varieties with log terminal singularities.
method Parabolic pluripotential theory and complex Monge-Ampère equations.
result Establishes a parabolic theory analogous to Bedford-Taylor's.
The study proves a key inequality for specific types of three-dimensional spaces.
problem Establishing a mathematical inequality for a specific class of three-dimensional spaces.
method Developed the orbifold version of the Bogomolov-Gieseker inequality for stable Q-sheaves on log terminal Kähler threefolds.
result Proved the Bogomolov-Gieseker inequality for log terminal Kähler threefolds.
Proves Kähler-Ricci shrinkers are complex analytic varieties.
problem Characterizing singular Kähler-Ricci shrinkers.
method Analyzes limits of Kähler-Ricci flows and applies algebraic geometry.
result Singular Kähler-Ricci shrinkers are locally algebraic complex-analytic varieties.
New findings on Kähler-Einstein currents dominating Kähler forms on compact spaces.
problem Understanding Kähler-Einstein currents on singular spaces.
method Analyzing currents' properties and applying them to compact spaces with log terminal singularities.
result Kähler-Einstein currents dominate Kähler forms on compact spaces with log terminal singularities.
Study on singularities of Chern-Ricci flow on complex manifolds.
problem Understanding finite-time singularities of the Chern-Ricci flow.
method Extending Guedj-Lu's approach to establish uniform a priori estimates for degenerate complex Monge-Ampère equations, applied to Chern-Ricci flows on complex log terminal varieties.
result Showed solutions starting from positive currents are smooth outside some analytic subset.
Study properties of algebraic threefolds with specific singularities.
problem Characterize and classify algebraic threefolds with certain singularities.
method Use topological invariants, rational homology, Poincaré duality, and Lie algebras.
result Relate topological invariants to Lie algebras and representations.
The paper proves ACC for local volumes under boundedness conditions.
problem Proving the ACC conjecture for local volumes of klt singularities.
method Analyzing klt singularities with bounded ambient germs.
result ACC conjecture for local volumes holds under bounded conditions.
We solve a class of control problems with fuel constraint by means of the log-Laplace transforms of -functionals of Dawson-Watanabe superprocesses. This solution is related to the superprocess solution of quasilinear parabolic PDEs with singular terminal condition. For the probabilistic verification proof, we develo…
Paper extends Hodge correspondence to singular Kähler spaces.
problem Establishing Hodge correspondence over Kähler spaces with singularities.
method Using equivalence of polystable Higgs bundles and semi-simple flat bundles over regular loci, and descent theorem for semistable Higgs bundles.
result Non-abelian Hodge correspondence established over compact Kähler klt spaces and their regular loci.
The paper discusses polynomial convergence to conical Kähler-Einstein metrics.
problem Understanding the convergence of Kähler-Einstein metrics to conical structures.
method Two-step degeneration theory and algebraic singularity analysis.
result Singular Kähler-Einstein metrics are conical if curvature grows quadratically near a point.
Proves K-stability of cubic threefolds and calculates their Kähler-Einstein metrics.
problem K-stability of cubic threefolds and explicit calculation of Kähler-Einstein metrics.
method Detailed study of three-dimensional canonical and terminal singularities, estimate of Kawamata log terminal volumes.
result All smooth cubic threefolds admit Kähler-Einstein metrics, and a precise list of singular KE ones is provided.
We prove the existence and uniqueness of Kähler-Einstein metrics on Q-Fano varieties with log terminal singularities (and more generally on log Fano pairs) whose Mabuchi functional is proper. We study analogues of the works of Perelman on the convergence of the normalized Kähler-Ricci flow, and of Keller, Rubinstein on…
Study numerical methods for singular FBSDEs with degenerate forward component.
problem Numerical approximation of singular fully coupled FBSDEs with degenerate forward component and non-smooth terminal condition.
method Splitting approach to treat diffusion and transport parts separately.
result The splitting method converges with rate 1/2 under structural condition.
A new algorithm discovers useful reinforcement learning options by focusing on termination compressibility.
problem Discovering useful reinforcement learning options.
method Proposes an algorithm that focuses on the termination condition, using a critic to learn the option transition model and optimize compressibility.
result The resulting options are non-trivial, meaningful, and useful for learning and planning.
The study of projective varieties with nef anticanonical divisors and log terminal singularities.
problem Understanding the structure and properties of projective varieties with specific divisor conditions.
method Analyzing the Albanese map and MRC fibration for klt projective varieties, showing locally constant fibrations and product decompositions.
result Generalization of results for smooth projective varieties to the klt case, including decomposition into rationally connected and projective varieties with trivial canonical divisor.
Survey on singularity theory and its relation to minimal model program.
problem Understanding singularities and their role in minimal model program.
method Construction and analysis of dual complexes, proof of ACC conjecture, local stability theory.
result Recent progress on local stability theory of Kawamata log terminal singularities.
Paper shows convergence of Fano Kähler-Ricci solitons without uniform Futaki invariant bound.
problem Degeneration of Fano Kähler-Ricci solitons without uniform Futaki invariant bound.
method Improves Phong-Song-Sturm's result by removing the uniform bound assumption.
result Convergence of Fano Kähler-Ricci solitons to a Kähler-Ricci soliton on a Q-Fano variety with log terminal singularities.
New method modifies diffusions for singular rewards.
problem Handling singular rewards in diffusions.
method Malliavin calculus for non-differentiable rewards.
result Stable and reliable training of diffusions.
We prove the existence and uniqueness of the weak Kahler-Ricci flow on projective varieties with log terminal singularities. It is also shown that the weak Kahler-Ricci flow can be uniquely continued through divisorial contractions and flips if they exist. We then propose an analytic version of the Minimal Model Progra…
Researchers prove birational invariance of BCOV invariant using motivic integration.
problem Proving the birational invariance of BCOV invariant for Calabi-Yau manifolds and varieties.
method Motivic integration theory applied to Calabi-Yau varieties with Kawamata log terminal singularities.
result Birational Calabi-Yau manifolds have the same BCOV invariant.
Measure preserving holomorphic vector fields, invariant anti-canonical divisors and Gibbs stabilitymath.AG
Holomorphic vector fields and anti-canonical divisors on complex manifolds are studied.
problem Existence of non-trivial holomorphic vector fields on compact complex manifolds.
method Vanishing result for measure preserving holomorphic vector fields, Gibbs stability, and log terminal singularities.
result No non-trivial holomorphic vector fields on compact complex manifolds with big anti-canonical line bundle.
Study shows nonextendibility of warped spacelike singularities in specific spacetimes.
problem Nonextendibility of warped spacelike singularities in specific spacetimes.
method Establishes a local obstruction through integrability conditions and radial compression.
result Imply -inextendibility for the one-horizon Birmingham-Kottler family.
Efficiently simulates SABR model with novel sampling methods.
problem Sampling integrated variance and terminal forward price in SABR model.
method Moment-matched shifted lognormal approximation for integrated variance, CEV approximation for terminal forward price.
result Enhanced simulation scheme is highly efficient, accurate, and reliable.
Develops parabolic pluripotential theory for complex flows.
problem Complex Monge-Ampère equations in degenerate settings.
method Study of semi-concave envelopes and unique solutions.
result Shows semi-concave envelopes as unique solutions.
Proves stable degeneration preserves symplectic forms and confirms Kaledin's conjecture.
problem Symplectic singularities and their degenerations.
method Combining volume minimization, deformation theory, and rigidity results.
result Kaledin's conjecture confirmed for symplectic singularities.
Method interpolates option prices and volatilities without arbitrage.
problem Interpolating option prices and volatilities without arbitrage.
method Sparse modeling approach based on integral equations and SVD.
result Flexible and efficient framework for arbitrage-free interpolation.
Compact RCD spaces derived from singular Kahler metrics on 3D projective varieties.
problem Understanding geometric structures of singular Kahler spaces.
method Proving RCD spaces homeomorphic to 3D projective varieties with bounded Nash entropy and Ricci curvature.
result Compact RCD spaces are equivalent to underlying projective varieties.
Deep learning solves PDEs with boundary conditions for barrier options.
problem Solving PDEs with boundary conditions for barrier options.
method Employing deep learning to approximate solutions of the PDE with boundary conditions.
result Deep learning can solve PDEs with boundary conditions for barrier options.
Resource allocation improved using machine learning from terminal positions.
problem Optimizing resource allocation in next-gen wireless systems with fast-changing channel conditions.
method Supervised machine learning using position information of mobile terminals.
result Coordinates-based resource allocation performs similarly to traditional CSI-based methods.
Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book Fouque, Papanicolaou, Sircar and Sølna (2011, CUP) analyzes models in which the volatility of the underlying i…