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.
Study optimal liquidation with multiple regimes using BSDEs with singular terminal values.
This paper establishes the existence of a unique nonnegative continuous viscosity solution to the HJB equation associated with a Markovian linear-quadratic control problems with singular terminal state constraint and possibly unbounded cost coefficients. The existence result is based on a novel comparison principle for…
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…
We study an optimal execution problem in illiquid markets with both instantaneous and persistent price impact and stochastic resilience when only absolutely continuous trading strategies are admissible. In our model the value function can be described by a three-dimensional system of backward stochastic differential eq…
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…
Proves finite step termination of Kähler-Einstein metric singularity formation.
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 orbifold singularities for Ricci-flat metrics on certain Kähler varieties.
Proof of complex geometry theorem for specific singular spaces.
Researchers find Kähler-Einstein metrics near isolated log terminal singularities.
Researchers prove birational invariance of BCOV invariant using motivic integration.
We consider the stochastic control problem of a financial trader that needs to unwind a large asset portfolio within a short period of time. The trader can simultaneously submit active orders to a primary market and passive orders to a dark pool. Our framework is flexible enough to allow for price-dependent impact func…
Proves finitely generated graded rings for klt singularities.
We prove that the sum of the -invariants of two different Kollár components of a Kawamata log terminal singularity is less than .
Constructs Kahler-Einstein metrics near isolated log canonical singularities.
Study two types of singular Kähler-Einstein metrics on complex varieties.
The paper finds optimal threshold strategies for insurance companies with a positive terminal value at creeping ruin.
The study proves a key inequality for specific types of three-dimensional spaces.
Proves Kähler-Ricci shrinkers are complex analytic varieties.
New findings on Kähler-Einstein currents dominating Kähler forms on compact spaces.
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…
We study an optimal liquidation problem under the ambiguity with respect to price impact parameters. Our main results show that the value function and the optimal trading strategy can be characterized by the solution to a semi-linear PDE with superlinear gradient, monotone generator and singular terminal value. We also…
Study on singularities of Chern-Ricci flow on complex manifolds.
We prove the K-moduli space of cubic threefolds is identical to their GIT moduli. More precisely, the K-(semi,poly)-stability of cubic threefolds coincide to the corresponding GIT stabilities, which could be explicitly calculated. In particular, this implies that all smooth cubic threefolds admit Kähler-Einstein metric…
New method modifies diffusions for singular rewards.
Paper extends Hodge correspondence to singular Kähler spaces.
The paper discusses polynomial convergence to conical Kähler-Einstein metrics.
Is an option to early terminate a swap at its market value worth zero? At first sight it is, but in presence of counterparty risk it depends on the criteria used to determine such market value. In case of a single uncollateralised swap transaction under ISDA between two defaultable counterparties, the additional unilat…
We provide representations of solutions to terminal value problems of inhomogeneous Black-Scholes equations and studied such general properties as min-max estimates, gradient estimates, monotonicity and convexity of the solutions with respect to the stock price variable, which are important for financial security prici…
To improve the efficient frontier of the classical mean-variance model in continuous time, we propose a varying terminal time mean-variance model with a constraint on the mean value of the portfolio asset, which moves with the varying terminal time. Using the embedding technique from stochastic optimal control in conti…
We survey some recent topics on singularities, with a focus on their connection to the minimal model program. This includes the construction and properties of dual complexes, the proof of the ACC conjecture for log canonical thresholds and the recent progress on the `local stability theory' of an arbitrary Kawamata log…
Extends results on smoothability of singular Fano and Calabi-Yau varieties.
The study of projective varieties with nef anticanonical divisors and log terminal singularities.
This paper works out fair values of stock loan model with automatic termination clause, cap and margin. This stock loan is treated as a generalized perpetual American option with possibly negative interest rate and some constraints. Since it helps a bank to control the risk, the banks charge less service fees compared …
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…
Geometrically interpolates rigid body motions with initial and terminal twists.
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…
In this paper we consider two problems on optimal implementation delay of taxation with trade-off for spectrally negative Lévy insurance risk processes. In the first case, we assume that an insurance company starts to pay tax when its surplus reaches a certain level and at the termination time of the business there…
Holomorphic vector fields and anti-canonical divisors on complex manifolds are studied.
In this work, we consider the problem of autonomously discovering behavioral abstractions, or options, for reinforcement learning agents. We propose an algorithm that focuses on the termination condition, as opposed to -- as is common -- the policy. The termination condition is usually trained to optimize a control obj…
ETCNN uses neural networks to price American options accurately.
Method interpolates option prices and volatilities without arbitrage.
The paper analyzes portfolio selection with non-concave utility and transaction costs.
Study optimal portfolio choice with risk control for log-returns.
Proves stable degeneration preserves symplectic forms and confirms Kaledin's conjecture.
Compact RCD spaces derived from singular Kahler metrics on 3D projective varieties.
We develop a parabolic pluripotential theory on compact K{ä}hler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge-Amp{è}re equations. We provide a parabolic analogue of the celebrated Bedford-Taylor theory and apply it to the study of the K{ä}hler-Ricci flow on varieties with log te…
We study local, global and local-to-global properties of threefolds with certain singularities. We prove criteria for these threefolds to be rational homology manifolds and conditions for threefolds to satisfy rational Poincaré duality. We relate the topological Euler characteristic of elliptic Calabi-Yau threefolds wi…