Quantization-aware phase retrieval algorithm improves signal reconstruction accuracy.
problem Reconstructing signals from quantized phase measurements.
method Developed a rank-1 projection algorithm with consistency criterion using one-sided quadratic cost.
result The algorithm achieves higher reconstruction accuracy and is closer to the Cramér-Rao lower bound.
New methods improve online matrix optimization with reduced computational cost.
problem Online matrix optimization with operator norm constraints.
method Gradient-based prediction scheme with smoothed potentials for nuclear norm.
result Adaptive matrix optimizers match Shampoo's regret up to a constant factor.
Research shows quadratic growth in derivative maxima for certain interval diffeos with parabolic fixed points.
problem Analyzing the growth of derivative maxima for C2 interval diffeomorphisms with parabolic fixed points. method Examining C2 diffeomorphisms with only parabolic fixed points, focusing on tangency and repelling behavior. result Maximal growth of derivative maxima is exactly quadratic for diffeomorphisms with a non-quadratic tangency to identity at a repelling fixed point.
The study examines portfolio optimization with quadratic transaction costs, complicating the optimization process.
problem Portfolio optimization with quadratic transaction costs is more challenging than with linear costs.
method Introduced numerical algorithms to solve the optimization problem with quadratic transaction costs.
result Quadratic transaction costs significantly impact the expected returns of optimized portfolios.
Optimal liquidation strategy for a risk-averse investor in a one-sided limit order book driven by a Levy process.
problem Balancing market risk and execution cost for a large share liquidation.
method Modeling the price process as a Levy process and solving a singular two-dimensional optimisation problem.
result Explicit expression for the optimal intervention boundary.
The paper solves a utility-based hedging problem with quadratic costs.
problem Optimal trading strategy for hedging European contingent claims with quadratic transaction costs.
method Duality theory applied to exponential utility maximization problem.
result Explicit computation of optimal trading strategy for quadratic payoffs.
We define a notion of Hempel distance for one-sided Heegaard splittings and show that the existence of alternate surfaces restricts distance for one-sided splittings in a manner similar to Hartshorn's and Scharlemann-Tomova's results for two-sided splittings. We also show that every geometrically compressible one-sided…
Study how transaction costs impact stock returns and holdings in equilibrium.
problem Impact of quadratic transaction costs on equilibrium stock returns and holdings.
method Developed a continuous-time risk-sharing model with FBSDEs to characterize equilibrium stock holdings and trading rates.
result Equilibrium stock holdings and trading rates are uniquely determined by FBSDEs, and equilibrium return by a system of coupled FBSDEs.
We reconsider the problem of optimal trading in the presence of linear and quadratic costs, for arbitrary linear costs but in the limit where quadratic costs are small. Using matched asymptotic expansion techniques, we find that the trading speed vanishes inside a band that is narrower than in the absence of quadratic …
We introduce a longevity feature to the classical optimal dividend problem by adding a constraint on the time of ruin of the firm. We extend the results in \cite{HJ15}, now in context of one-sided Lévy risk models. We consider de Finetti's problem in both scenarios with and without fix transaction costs, e.g. taxes. We…
When a Dehn filled link manifold contains a geometrically incompressible one-sided surface, it is shown there is a unique boundary incompressible position that the surface can take in the link space. The proof uses a version of the sweep-out technique from two-sided Heegaard splitting theory. When applied to one-sided …
Study insider trading benefits in a market with high transaction costs.
problem Super--replication of European contingent claims in illiquid markets.
method Model insider information and quadratic transaction costs, analyze scaling limits.
result Scaling limit gives the value of insider information.
In this paper we prove an extrinsic one-sided curvature estimate for disks embedded in R3 with constant mean curvature which is independent of the value of the constant mean curvature. We apply this extrinsic one-sided curvature estimate in [24] to prove to prove a weak chord arc type result for these disks…
The paper develops an expansion for optimizing portfolios with small quadratic transaction costs.
problem Optimizing portfolios with small, instantaneous, quadratic transaction costs.
method Develops an asymptotic expansion for the Hamilton-Jacobi-Bellman equation.
result Derives explicit formulae for the first two terms of the expansion.
Study liquidity dynamics in dealer markets with quadratic costs.
problem Understanding price formation in dealer markets with liquidity costs.
method Solve for competitive equilibrium prices in a continuous-time model with quadratic inventory costs.
result Endogenous transient price impact due to gradual position transfer.
Proves c-concavity condition for transport maps on manifolds.
problem Optimality of transport maps on Riemannian manifolds.
method Analyzes the condition abla2f<g and its implications for c-concavity. result Sufficient condition for optimality of transport maps.
Using basic properties of one-sided Heegaard splittings, a direct proof that geometrically compressible one-sided splittings of RP^3 are stabilised is given. The argument is modelled on that used by Waldhausen to show that two-sided splittings of S^3 are standard.
Proposes a new framework for invariant quadratic P&L predictions in option books.
problem Inconsistent second-order P&L predictions across different factor parameterizations.
method Local, model-agnostic framework using covariant Hessian defined by an affine connection.
result Coordinate-invariant quadratic P&L predictions that match desk targets.
The paper extends a variance gamma model to quadratic functions, reducing arbitrage and computational costs.
problem Creating an arbitrage-free interpolation for option pricing models.
method Generalizing the local variance gamma model to a piecewise quadratic local variance function.
result The quadratic model results in an arbitrage-free interpolation of class C3, reducing knots and computational cost.
OMGD algorithm optimizes online convex optimization with switching costs and delayed gradients.
problem Optimizing online convex optimization with switching costs and delayed gradients.
method Proposed an online multiple gradient descent (OMGD) algorithm for quadratic and linear switching costs.
result OMGD achieves optimal dynamic regret in the limited information setting.
NOT learns optimal transport plans, kernel costs improve performance.
problem NOT algorithm learns non-optimal plans with weak quadratic costs.
method Introduced kernel weak quadratic costs to improve NOT's performance.
result Kernel costs provide improved theoretical and practical guarantees.
Optimal contracts are found for agents with quadratic effort costs.
problem Finding optimal contracts in principal-agent problems with quadratic effort costs.
method Modeling the problem using Hamilton-Jacobi-Bellman (HJB) equations and proving the existence of classical solutions.
result Existence of optimal contracts for agents with quadratic effort costs is proven.
Study cost-driven state representation learning for control from partial observations.
problem Learning state representation for control from partial and high-dimensional observations.
method Cost-driven state representation learning via predicting cumulative costs.
result Established finite-sample guarantees for near-optimal representation and controller.
We study minimal graphic functions on complete Riemannian manifolds $\Si$ with non-negative Ricci curvature, Euclidean volume growth and quadratic curvature decay. We derive global bounds for the gradients for minimal graphic functions of linear growth only on one side. Then we can obtain a Liouville type theorem with …
Schrödinger bridge solved with Weyl calculus for quadratic state cost.
problem Optimal control policy to steer joint state statistics.
method Weyl calculus in quantum mechanics for reaction-diffusion PDEs.
result Explicit Markov kernel for quadratic state cost found.
The stability and the index of complete one-sided minimal surfaces of certain three-dimensional Riemannian manifolds with positive scalar curvature are studied.
Model liquidity premia using a risk-sharing economy with quadratic costs.
problem Understanding the cross-section of liquidity premia earned by assets with different trading costs.
method Developed a risk-sharing economy model with quadratic transaction costs, leading to matrix-valued Riccati equations for equilibrium.
result Calibrated model to time series data, revealing liquidity premia across assets with varying trading costs.
Adam-type optimizers show one-sided convergence in GAN training, not reaching critical points.
problem Theoretical understanding of Adam-type optimizers in non-convex non-concave min-max optimization.
method Empirical and theoretical analysis of Adam-type algorithms' convergence in GAN training.
result Adam-type algorithms converge to one-sided first order stationary points under the one-sided MVI condition.
RL and DTSOC for final quadratic hedging performance studied.
problem Optimal hedging of European call options with and without transaction costs.
method Reinforcement Learning and Deep Trajectory-based Stochastic Optimal Control.
result RL and DTSOC perform similarly to variance-optimal hedging in various market models.
Paper optimizes broker performance by estimating execution costs.
problem Minimizing execution costs for large trades.
method Intraday modeling of execution cost components (linear and quadratic).
result Substantial improvements in estimating execution costs.
Study analyzes market equilibrium returns with price impact and transaction costs.
problem Modeling equilibrium returns in markets with strategic order placement and transaction costs.
method Analyzes frictionless and transaction-cost markets, characterizes Nash equilibrium via FBSDEs.
result Equilibrium returns are affected by transaction costs, especially with noise traders.
In the closed, non-Haken, hyperbolic class of examples generated by (2p,q) Dehn fillings of Figure 8 knot space, the geometrically incompressible one-sided surfaces are identified by the filling ratio p/q and determined to be unique in all cases. When applied to one-sided Heegaard splittings, this can be used to classi…
Various structural properties are developed for non-orientable surfaces in link spaces. The Möbius band tree is described to represent genus growth of one-sided surfaces in solid tori. The structure of the Tree allows various insights into the change of genus under boundary slope, which are not possible using the exist…
New toolkit classifies hazardous solvents from Raman spectra.
problem Separating hazardous chlorinated solvents from other materials.
method One-sided classification algorithms designed for rare or absent outliers.
result One-sided classifiers are more robust when test data is from a different distribution.
Non-bilinear observations make optimal control harder, showing non-convex costs and non-affine optimal controllers.
problem Optimal control from bilinear observations in linear systems is challenging.
method Analytical and numerical methods to study the non-convex cost-to-go and non-affine optimal controllers.
result The Separation Principle does not hold for bilinear observations, leading to non-convex costs and non-affine optimal controllers.
Study non-orientable surfaces to find loops winding around punctures.
problem Understanding loops winding around punctures on non-orientable surfaces.
method Analyzing one-sided geodesics and their powers on non-orientable surfaces.
result Loops can wind around a puncture at most two values of m for odd m. We give a sufficient and necessary condition of the fundamental group homomorphism of a map between manifolds to induce homology equivalences. Moreover, a classification of one-sided h-cobordism of manifolds up to diffeomorphisms is obtained, based on Quillen's plus construction with Whitehead torsions.
Left orderability proven for certain 3-manifolds with specific foliations.
problem Proving left orderability for specific 3-manifolds with taut foliations.
method Analyzing the fundamental group of a 3-manifold with a co-orientable taut foliation.
result The fundamental group of the 3-manifold is left orderable.
Study removes singularities from area-minimizing surfaces.
problem Removal of singularities from area-minimizing surfaces.
method Extending results on area-minimizing cones to handle isolated singularities.
result Isolated singularities can be locally perturbed away on the minimizing side.
A new scheme reduces global search cost by a square root factor.
problem Challenges in finding global minimum of cost functions.
method Gradient descent combined with a biased crossover of two good solutions.
result Quadratic speedup of global search efficiency.
Actor-critic finds Nash in mean-field games with linear-quadratic costs.
problem Finding Nash equilibrium in mean-field Markov games with linear dynamics and quadratic costs.
method Mean-field actor-critic algorithm with linear function approximation.
result Algorithm converges linearly to Nash equilibrium.
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. A new method for selective classification trades off accuracy for coverage.
problem Selective classification allows a classifier to abstain from predicting some instances.
method Optimizes a collection of class-wise decoupled one-sided empirical risks.
result The method achieves near-optimal coverage in high target accuracy regimes.
Study risk-sharing equilibria with general transaction costs, proving mean-reversion of returns.
problem Analyzing risk-sharing equilibria with general convex transaction costs.
method Infinite-horizon model with linear state dynamics, solved numerically using deep learning.
result Equilibrium returns mean-revert around frictionless counterparts, with different dynamics for quadratic and proportional costs.
Study one-sided matrix completion with two observations per row.
problem Recover right singular vectors of a low-rank matrix X with few observations. method Impute missing values of XTX and analyze recovery guarantees. result Provable recovery of XTX with Ω(r2dlogd) rows, outperforming standard methods. Study learns state representations from observations for control, proving guarantees.
problem Learning state representations from high-dimensional observations for control.
method Cost-driven approach, learning latent state model to predict costs.
result Proves finite-sample guarantees for near-optimal state representation and controller.
Poyiadjis et al. (2011) show how particle methods can be used to estimate both the score and the observed information matrix for state space models. These methods either suffer from a computational cost that is quadratic in the number of particles, or produce estimates whose variance increases quadratically with the am…
Investigates VaR behavior for sums of one-sided random variables, showing impossibilities and conditions for super-additivity.
problem Investigates the behavior of Value-at-Risk (VaR) for sums of one-sided random variables.
method Analyzes the extremal aggregation behavior of VaR, introduces structural conditions for super-additivity.
result Characterizes when VaR is fully super-additive and provides unified framework for various dependence structures.