The paper explains the concave shape of yield curves from trading perspectives.
problem Lack of explanation for the concavity of yield curves from economics theory.
method Explains the concavity of yield curves from trading perspectives.
result Offers an explanation for the concave shape of yield curves.
Study minimax risk of score estimation for log-concave distributions.
problem Minimizing risk in score estimation for log-concave distributions.
method Developed subclasses of log-concave densities and constructed a locally adaptive, multiscale estimator.
result Established minimax rates for score estimation over specific subclasses of log-concave densities.
Active-set algorithm improves Cox regression for shape-restricted covariates.
problem Improving Cox regression for shape-restricted covariates.
method Shape-restricted inference using active-set optimization for spline basis expansion.
result Active-set algorithm produces accurate linear covariate effect estimates.
We solve S-shaped utility portfolio selection with SD constraints using algorithms and neural networks.
problem Optimizing portfolios with S-shaped utility functions under SD constraints.
method First-order SD constraint solution, numerical algorithm for SSD, neural network approach.
result Effective numerical and neural network solutions for SSD constrained problems.
A convex surface contracting by a strictly monotone, homogeneous degree one function of curvature remains smooth until it contracts to a point in finite time, and is asymptotically spherical in shape. No assumptions are made on the concavity of the speed as a function of principal curvatures.
We consider market players with tail-risk-seeking behaviour as exemplified by the S-shaped utility introduced by Kahneman and Tversky. We argue that risk measures such as value at risk (VaR) and expected shortfall (ES) are ineffective in constraining such players. We show that, in many standard market models, product d…
New star-shaped acceptability indexes generalize existing methods.
problem Generalizing existing acceptability measures.
method Characterizing acceptability indexes through star-shaped risk measures and sets.
result Introducing concrete examples linked to various financial measures.
The paper studies how arm selection in a bandit problem changes with shape constraints.
problem Stochastic Thresholding Bandit Problem under shape constraints.
method Investigation of TBP under four shape constraints: monotonic increasing, unimodal, concave, and fixed.
result Minimax rates for regret vary significantly depending on the shape constraint.
A new method for pricing options with flexible volatility shapes.
problem Parameterizing risk-neutral distributions for accurate option pricing.
method Parsimonious and interpretable parameters for direct control over implied volatility curves.
result Accurate calibration across a large dataset of option curves.
ICCNLS models complex relationships as convex and concave components.
problem Complex input-output relationships with affine ambiguity.
method Sub-gradient constrained affine functions, global orthogonality constraints, L1, L2, and elastic net regularisation.
result Improved predictive accuracy and model simplicity compared to conventional methods.
This study proves new financial market theorems breaking standard risk definitions.
problem Breaking standard risk definitions in financial markets.
method Presenting proofs for new financial market theorems.
result New definitions are richer and broader than standard ones considering shape.
In this study, we extend the optimal execution problem with convex market impact function studied in Kato (2014) to the case where the market impact function is S-shaped, that is, concave on [0,xˉ0] and convex on [xˉ0,∞) for some xˉ0≥0. We study the corresponding Hamilton-Jacobi-…
Dynamic pricing policy converges to Nash equilibrium with low regret.
problem Sequential price competition among sellers over multiple periods.
method Semi-parametric least-squares estimation of s-concave demand functions.
result Prices converge to Nash equilibrium with rate O(T−1/7) and sellers incur regret O(T5/7). A new algorithm uses concavity in Gaussian processes to optimize decisions in bandit problems.
problem Optimizing decisions in sequential problems with context-dependent rewards.
method Proposes a UCB algorithm using a shape-constrained reward function estimator based on a Gaussian Process model with concavity constraints.
result Derives regret bounds for the proposed UCB algorithm.
Estimates self- and cross-impact concavity and decay patterns in financial markets.
problem Understanding the impact of financial transactions on market dynamics.
method Nonparametric estimation of concave multi-asset propagator models using metaorders and order flow data.
result Concave self-impact with shifted power-law decay, significant gain from cross-impact, and improved predictive accuracy.
Study optimal consumption for loss-averse agents considering past spending peaks.
problem Optimal consumption for loss-averse agents with reference to past spending maximum.
method Adopted S-shaped utility, concave envelope, HJB variational inequality, dual transform, and smooth-fit conditions.
result Obtained piecewise closed-form solutions for optimal consumption and investment control.
Develops deep learning methods for solving S-shaped utility maximisation problems.
problem Optimizing portfolios with S-shaped utility and random benchmarks.
method Uses deep learning and duality methods to solve the Hamilton-Jacobi-Bellman equation and adjoint equation.
result Demonstrates the accuracy of deep learning methods for non-concave utility maximisation problems.
Decision maker's preferences are often captured by some choice functions which are used to rank prospects. In this paper, we consider ambiguity in choice functions over a multi-attribute prospect space. Our main result is a robust preference model where the optimal decision is based on the worst-case choice function fr…
New flow expands hypersurfaces in hyperbolic space, showing round limiting shape for certain powers.
problem Understanding the limiting shape of hypersurfaces expanding in hyperbolic space.
method Introduced shifted inverse curvature flow with positive power p for a smooth curvature function. result For 0<p≤1, limiting shape is always round as maximal existence time is approached. The paper studies how the shape of surfaces changes over time using curvature.
problem Understanding how the shape of surfaces evolves over time using curvature.
method The authors use curvature flow with a power of a function of principal curvatures to study the evolution of surfaces.
result The complete smooth strictly convex solution exists and remains a graph until the maximal time of existence.
In this paper, we first investigate the flow of convex surfaces in the space form R3(κ) (κ=0,1,−1) expanding by F−α, where F is a smooth, symmetric, increasing and homogeneous of degree one function of the principal curvatures of the surfaces and the power α∈(0,1] for κ=0,−1 and α=1 for κ=1…
We analyze a nonlinear equation proposed by F. Black (1968) for the optimal portfolio function in a log-normal model. We cast it in terms of the risk tolerance function and provide, for general utility functions, existence, uniqueness and regularity results, and we also examine various monotonicity, concavity/convexity…
Ancient convex solutions to flow equations are limited to simple shapes.
problem Characterizing ancient convex solutions to flow equations.
method Analyzing mean curvature flow and curvature functions of convex hypersurfaces.
result Ancient convex solutions to flow equations are limited to spherical, cylindrical, or planar shapes.
Investigates probability of error in structured thresholding bandit problems.
problem Probability of misclassifying arms in structured thresholding bandit problems.
method Analyzes two shape constraints: monotonic increasing and concave sequences of arm means.
result Upper and lower bounds for the probability of error match up to constants in the problem dependent regime.
Study on efficiency in economies with risk-averse agents, finding Pareto optima.
problem Efficiency in economies with risk-averse agents.
method Analysis of utility functionals, existence and characterization of Pareto optima.
result Existence and comonotone characterization of Pareto optima for risk-averse agents.
Investigates portfolio selection with transaction costs and stochastic volatility, using deep learning for computation.
problem Optimal portfolio selection with transaction costs and stochastic volatility.
method Two-factor stochastic volatility model, option-implied utility function, deep learning policy iteration.
result Deep learning method effectively computes optimal investment decisions under transaction costs and stochastic volatility.
We propose a computationally efficient random walk on a convex body which rapidly mixes and closely tracks a time-varying log-concave distribution. We develop general theoretical guarantees on the required number of steps; this number can be calculated on the fly according to the distance from and the shape of the next…
We develop a theory for the market impact of large trading orders, which we call metaorders because they are typically split into small pieces and executed incrementally. Market impact is empirically observed to be a concave function of metaorder size, i.e., the impact per share of large metaorders is smaller than that…
In stochastic portfolio theory, a relative arbitrage is an equity portfolio which is guaranteed to outperform a benchmark portfolio over a finite horizon. When the market is diverse and sufficiently volatile, and the benchmark is the market or a buy-and-hold portfolio, functionally generated portfolios introduced by Fe…
Concave elliptic operators yield concave functions on cohomology.
problem Understanding concave functions on cohomology.
method General construction of concave elliptic operators.
result Generalized Khovanskii-Teissier inequalities.
The paper establishes conditions for strict power concavity in convolutions.
problem Conditions for strict power concavity in convolutions.
method Analyzes sufficient conditions for strict parabolic power concavity of convolutions.
result Establishes sufficient conditions for strict power concavity of convolutions.
Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. In this work we show how shape constraints such as convexity/concavity and their extensions, can be integrated into additive models. The proposed sparse difference of convex additive models (SDCAM) can est…
Investigates conditions for risk or utility functionals to be sensitive to large losses.
problem Conditions for risk or utility functionals to be sensitive to large losses.
method Analyzes sensitivity to large losses for various risk and utility functionals.
result Value at Risk and Expected Shortfall generally fail to be sensitive to large losses, but expected utility functionals and certain adjusted versions are sensitive.
This paper analyzes optimal consumption strategies for loss-averse investors with multiplicative habit formation.
problem Optimal consumption strategies for loss-averse investors with multiplicative habit formation.
method The study uses a concave envelope of the S-shaped utility function and a nonlinear free boundary problem to analyze the HJB equation.
result The paper provides optimal consumption and investment policies in feedback form.
Minimal graph level sets are concave if boundary is concave.
problem Understanding curvature of minimal graph level sets.
method Proved an inequality and showed geometric properties.
result Level sets of minimal graphs are concave if boundary is concave.
Simple connection between Harnack inequalities and concavity of arrival time functions.
problem Proving differential Harnack inequalities for various flows.
method Directly proving concavity properties of time-of-arrival functions for a class of flows using a concavity maximum principle.
result Short proof of Hamilton's and Andrews' differential Harnack inequalities.
Proves log-concavity of cluster algebra coefficients for type An.
problem Log-concavity of cluster algebra coefficients.
method Introduced atomic theta basis and proved log-concavity for type An. result Proved log-concavity of coefficients for cluster algebra variables of type An. Study improves sampling from non-log-concave distributions using Fisher information.
problem Sampling from non-log-concave distributions with high Fisher information guarantees.
method Proximal sampler with RGO implementation, leveraging log-concave sampling results.
result Improved complexity guarantee in relative Fisher information for non-log-concave sampling.
The amoebas associated to algebraic varieties are certain concave regions in the Euclidean space whose shape reminds biological amoebas. This term was formally introduced to Mathematics in 1994 by Gelfand, Kapranov and Zelevinski. Some traces of amoebas were appearing from time to time, even before the formal introduct…
Established concavity principle for curved spaces.
problem Solving equations on curved spaces with nonnegative curvature.
method Applied concavity principle to elliptic and parabolic equations on locally symmetric spaces with nonnegative curvature.
result First general concavity principle on spaces with non-constant sectional curvature.
Establishes log-concavity estimates for convex domains' first Dirichlet eigenfunctions.
problem Quantifying the Hessian of log-concave eigenfunctions on convex domains.
method Analyzes log-concavity properties of the first Dirichlet eigenfunction on convex domains.
result Obtains quantitative estimates for the Hessian of logu. Novel framework for portfolio selection considering utility and risk.
problem Maximizing utility subject to risk constraints with various utility and risk functionals.
method General framework accommodating non-concave utilities and non-convex risk measures. Characterization of well-posedness using a simple either-or criterion.
result Minimal condition for well-posedness: either utility or risk must be sensitive to large losses.
New saddle network architectures preserve convex-concave geometry in optimization problems.
problem Optimization models with convex x and concave y components.
method Structured separable decomposition and saddle network architectures.
result Proven one-dimensional approximation theorem and high accuracy on various test functions.
Investigates concavity of spacetimes, showing conditions for local concavity.
problem Understanding the concavity of spacetimes in Finsler geometry.
method Analyzes flag curvature and future capsules to characterize concavity.
result Berwald spacetimes are locally concave if and only if their flag curvature is nonnegative in timelike directions.
Heat flow fails to preserve concavity in curved spaces.
problem Non-preservation of concavity properties in curved spaces.
method Analysis of Dirichlet heat flow on Riemannian manifolds.
result No concavity properties are preserved unless curvature is zero.
The paper constructs random concave functions on the unit simplex.
problem Understanding probability measures on spaces of concave functions.
method Constructing random concave functions via a scaled minimum of random hyperplanes.
result There is a transition from deterministic to non-trivial limiting distributions as the number of hyperplanes increases.
We define a class of L-convex-concave subsets of RPn, where L is a projective subspace of dimension l in RPn. These are sets whose sections by any (l+1)-dimensional space L' containing L are convex and concavely depend on L'. We introduce an L-duality for these sets, and prove that the L-dual to an L-…
Geodesic concavity and hypersymplectic structures in G2-structures space.
problem Analyzing the geodesic concavity and hypersymplectic structures in the space of closed G2-structures. method Utilising the geodesic constructed in the previous article, we show geodesic concavity and decrease in length of G2 Laplacian flow. result Hitchin's volume functional is geodesically concave and the G2 Laplacian flow decreases the length.