Derives portfolio dynamics using retarded action principle.
problem Modeling self-financing portfolio dynamics with causality.
method Retarded action principle for differential representation.
result Consistent representation of portfolio dynamics.
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48 results for “retarded action principle”
Formula for Hadamard coefficients from Green's operators on spacetimes.
problem Calculating Hadamard coefficients from Green's operators on spacetimes.
method Developed formulas for diagonal values and integrals over the diagonal of Hadamard coefficients.
result Formulated analogues of Hadamard expansions and resolvents for Green's operators.
The paper derives expansions for Green's operators and resolvents using Hadamard methods.
problem Analyzing normally hyperbolic operators and their Green's functions.
method Hadamard expansions for powers of Green's operators and resolvents.
result Derives expansions involving Hadamard coefficients for advanced/retarded Green's operators.
An agent-based model for firms' dynamics is developed. The model consists of firm agents with identical characteristic parameters and a bank agent. Dynamics of those agents is described by their balance sheets. Each firm tries to maximize its expected profit with possible risks in market. Infinite growth of a firm dire…
In this short paper, we review recent progress on the positive mass theorem for spacelike hypersurfaces which approach to null infinity in asymptotically flat spacetimes. We use it to prove, if the functions , vanish at certain retarded time in vacuum Bondi's radiating spacetimes, then the Bond…
Reduction principles for proper actions on smooth manifolds.
problem Proper actions on smooth manifolds and their properties.
method Exhibit constructions and prove reduction principles for proper actions.
result Reduction principles hold for proper actions, polar actions, and copolarity.
Holographic principle matches deformed Liouville theory action.
problem Matching deformed Liouville theory action in holography.
method Developed a holographic scheme involving bending energy.
result Perfect match between deformed theory actions on field and gravity sides.
Local-to-global principle for Morse actions on symmetric spaces.
problem Recognizing Morse actions on symmetric spaces.
method Equivariant Morse quasiisometric embeddings of trees into symmetric spaces.
result Algorithmic recognizability of Morse actions and construction of Morse Schottky subgroups.
The paper explores new learning principles based on least cognitive action.
problem Formulating learning problems in a way that incorporates time and perception.
method Introduces the principle of least cognitive action and proves its well-posedness.
result Proves the existence of a minimum for a special form of cognitive action, leading to fourth-order differential equations of learning.
On the relation between ADM and Bondi energy-momenta III -- perturbed radiative spatial infinitygr-qc
In a vacuum spacetime equipped with the Bondi's radiating metric which is asymptotically flat at spatial infinity including gravitational radiation ({\bf Condition D}), we establish the relation between the ADM total energy-momentum and the Bondi energy-momentum for perturbed radiative spatial infinity. The perturbatio…
Study on symmetric hyperbolic systems with nonlocal potentials, proving well-posedness and existence of solutions.
problem Initial value problem for symmetric hyperbolic systems with nonlocal potentials.
method Analysis on globally hyperbolic Lorentzian manifolds, proving existence, uniqueness, and regularity of solutions.
result Established well-posedness of the Cauchy problem for symmetric hyperbolic systems with nonlocal potentials.
General Relativity can be reformulated as a diffeomorphism invariant SU(2) gauge theory. A new action principle for this "pure connection" formulation of GR is described.
Paper presents an action principle for Einstein-Weyl equations in 3D.
problem Finding an action principle for Einstein-Weyl equations.
method Metric affine f(R) gravity action plus additional terms involving Lagrange multipliers and gravitational Chern-Simons contributions.
result The Weyl vector dynamics is governed by a special case of the generalized monopole equation.
Green-hyperbolic operators are linear differential operators acting on sections of a vector bundle over a Lorentzian manifold which possess advanced and retarded Green's operators. The most prominent examples are wave operators and Dirac-type operators. This paper is devoted to a systematic study of this class of diffe…
Geometric derivation of Einstein equations from causal fermion systems.
problem Deriving Einstein's equations from a new theoretical framework.
method Analysis of causal fermion systems and causal action principle.
result Einstein equations derived from causal action principle.
We show that all vector bundles over CP^2 which are not spin admit a complete metric with nonnegative sectional curvature. In the proof we construct a nonnegatively curved metric on the corresponding principle bundle by showing that it admits a cohomogeneity one action with singular orbits of codimension 2. This is clo…
Reduces proper actions to simpler core actions for analysis.
problem Understanding properties of proper actions on manifolds.
method Extending Skjelbred and Straume's construction to non-compact groups, focusing on core of actions.
result Properties of proper actions are determined by simpler core actions.
Previous research has shown that for stock indices, the most likely time until a return of a particular size has been observed is longer for gains than for losses. We establish that this so-called gain/loss asymmetry is present also for individual stocks and show that the phenomenon is closely linked to the well-known …
The paper proposes a principle for dynamically adjusting the granularity of reinforcement learning abstractions.
problem Lack of general principles for dynamically adjusting the granularity of reinforcement learning abstractions.
method The paper proposes a principle based on rate-distortion theory, formalized through a performance certificate decomposing value error into learning and abstraction error bounds.
result Soft state-action abstractions can achieve near-optimal performance under substantial lossy compression of state and action information.
With the daily and minutely data of the German DAX and Chinese indices, we investigate how the return-volatility correlation originates in financial dynamics. Based on a retarded volatility model, we may eliminate or generate the return-volatility correlation of the time series, while other characteristics, such as the…
New Einstein manifolds split into symmetric and compact parts.
problem Understanding Einstein manifolds with unimodular isometry groups.
method Theory of polar actions, Lie-theoretic arguments, and maximum principles.
result Negative Einstein manifolds split into symmetric and compact parts.
Paper proposes a new learning principle based on least cognitive action.
problem Learning from temporal data, especially with time involved.
method Introduces a new learning principle based on the principle of Least Cognitive Action, which is better suited for temporal learning.
result The new principle leads to a learning process driven by differential equations, similar to natural laws.
New method learns influential action sequences without privileged final states.
problem Learning meaningful action sequences in large action spaces.
method Model-free approach that considers the full trajectory.
result Successfully applied to large action spaces.
New method QMLE performs well in complex action spaces without policy gradients.
problem Why policy gradients outperform action-value methods in complex action spaces.
method QMLE framework for action-value methods based on three principles.
result QMLE performs comparably to policy gradient methods in complex action spaces.
New principle optimizes bandit decisions with context.
problem Dealing with general function classes and large context spaces in bandits.
method Upper Counterfactual Confidence Bounds (UCCB) principle.
result Proves optimality and efficiency in complex settings.
Study of Bondi-Sachs formalism for massless scalar field with zero cosmological constant.
problem Analyzing the Bondi-Sachs formalism for Einstein's massless scalar field equations.
method Asymptotic expansions and peeling property for Bondi-Sachs metrics and scalar fields.
result Positivity of Bondi energy-momentum under specific conditions.
Quantum memristors created in photonic platforms with real-time control.
problem Creating quantum memristors for integrated quantum photonics.
method Designing a tunable beam splitter with real-time control, using weak measurements and classical feedback.
result Demonstrated that the tunable beam splitter behaves as a quantum memristor.
Internal Lagrangians derived from variational principles.
problem Reproducing the principle of stationary action in variational geometry.
method Introducing stationary points of internal Lagrangians, establishing connections with symmetries and conservation laws, and investigating relations between non-degenerate and internal Lagrangians.
result Noether's theorem reformulated in terms of internal Lagrangians.
We construct a large class of dynamical vacuum black hole spacetimes whose exterior geometry asymptotically settles down to a fixed Schwarzschild or Kerr metric. The construction proceeds by solving a backwards scattering problem for the Einstein vacuum equations with characteristic data prescribed on the event horizon…
Extending our reduction construction in \cite{Hu} to the Hamiltonian action of a Poisson Lie group, we show that generalized Kähler reduction exists even when only one generalized complex structure in the pair is preserved by the group action. We show that the constructions in string theory of the (geometrical) -dua…
We study the limit of quasilocal energy defined in [7] and [8] for a family of spacelike 2-surfaces approaching null infinity of an asymptotically flat spacetime. It is shown that Lorentzian symmetry is recovered and an energy-momentum 4-vector is obtained. In particular, the result is consistent with the Bondi-Sachs e…
The paper examines how risk reduction and insurance choices interact under convex premium principles.
problem Interaction between self-protection and insurance demand under convex premium principles.
method Investigates optimal prevention efforts and insurance shares using distortion risk measures.
result Self-protection and insurance are complementary, but ex ante moral hazard can turn this into a substitution effect.
Formulae track evolution of angular momentum and center of mass at null infinity.
problem Tracking the evolution of conserved quantities at null infinity.
method Evolution formulae in Bondi-Sachs coordinates, expressed in terms of shear and news tensors.
result Supertranslation invariance of fluxes, conservation law of angular momentum, duality paradigm.
Geodesics on Kähler manifold potentials are paths of least action.
problem Understanding geodesics on the space of Kähler potentials.
method Study Lagrangians and geodesics on the Fréchet manifold of Kähler potentials, showing geodesics are paths of least action.
result Geodesics on the space of Kähler potentials are paths of least action, and conversely under suitable conditions.
PredNet fails to fully adhere to predictive coding principles.
problem Evaluation of PredNet's adherence to predictive coding theory.
method Critical analysis of PredNet's architecture and performance on a video action classification dataset.
result PredNet does not fully follow predictive coding principles but shows potential with top-down conditioning.
Three methods for training models on bandit feedback, reviewed and tested.
problem Training machine learning models on recommender system logs.
method Three distinct methods: argmax, distribution adjustment, and inverse propensity score.
result The latter two methods violate principles but perform well in certain settings.
Paradan and Vergne generalised the quantisation commutes with reduction principle of Guillemin and Sternberg from symplectic to Spin-manifolds. We extend their result to noncompact groups and manifolds. This leads to a result for cocompact actions, and a result for non-cocompact actions for reduction at zero. The r…
The paper explores how organisms and machines learn from their environment using machine learning, information theory, and thermodynamics.
problem How organisms and machines adapt to their environment.
method Machine learning, information theory, and thermodynamics approaches to understanding and modeling adaptation.
result Unified view of adaptation in organisms and machines based on principles of machine learning, information theory, and thermodynamics.
We formulate a quantization commutes with reduction principle in the setting where the Lie group , the symplectic manifold it acts on, and the orbit space of the action may all be noncompact. It is assumed that the action is proper, and the zero set of a deformation vector field, associated to the momentum map and a…
The Reactive Volatility Modelq-fin.ST
We present a new volatility model, simple to implement, that includes a leverage effect whose return-volatility correlation function fits to empirical observations. This model is able to capture both the "retarded effect" induced by the specific risk, and the "panic effect", which occurs whenever systematic risk become…
Differential K-theory gets a -ring structure.
problem Establishing a -ring structure in differential K-theory.
method Splitting principle for differential K-theory, Adams operations construction.
result Differential -ring admits a -ring structure.
New principle for supersymmetric localization on Lie groups.
problem Computing supertrace of non-supersymmetric observables.
method Invariant supersymmetric deformations and fermionic zero modes.
result Path integral localizes to periodic orbits.
New metrics for SPD matrices explore affine invariance and symmetry principles.
problem Choosing appropriate metrics for SPD matrices based on invariance principles.
method Investigates power-affine and deformed-affine metrics within a continuum of SPD metrics.
result Introduces new families of metrics based on affine invariance and symmetry.
Study Liouville action on quasi-Fuchsian groups, proving formulas and relating to holography.
problem Analyzing Liouville action for quasi-Fuchsian groups with different types of elements.
method Derived formulas for classical Liouville action, proved first and second variations, and established holography principle.
result Established an equality linking Liouville action and renormalized volume for quasi-Fuchsian groups.
New approach uses physics principles to improve business analytics.
problem Current business analytics methods fail with new data.
method Divide KPIs into controllable and uncontrollable groups; apply physics principles to controllable ones.
result Improves understanding and optimization of controllable KPI dynamics.
Symplectic coordinates found on a Hitchin component for a hyperbolic surface.
problem Parametrizing the -Hitchin component with canonical coordinates.
method Proved global Darboux coordinates with half canonical Goldman coordinates.
result Global Darboux coordinates exist for the -Hitchin component.
Paper proves -semi-rigidity of meandering-hyperbolic actions.
problem Stability of meandering-hyperbolic actions in topology.
method Proves semi-rigidity using local -semi-rigidity.
result Every meandering-hyperbolic action is locally semi-rigid in topology.
The paper suggests asset prices follow physical laws, allowing for accurate price movement forecasts.
problem Predicting extreme price movements in financial markets.
method Modeling asset price dynamics as a harmonic oscillator and applying the principle of stationary action.
result The theory can make accurate forecasts of price movements during market crashes and specific price displacements at other times.