Introduces RPU to explain randomization preference in dynamic settings.
problem Explains preference for randomization in dynamic investment problems.
method Introduces recursive perturbed utility (RPU) to incorporate randomization preference.
result Proves RPU-optimal portfolio policy is Gaussian and can be expressed in closed form.
TechRank ranks companies and technologies based on investor preferences.
problem Estimating influence and ranking companies and technologies.
method Recursive algorithm based on a bi-partite graph with weighted nodes, incorporating investor preferences.
result Provides investors with a quantitative ranking of technologies for optimal portfolio design.
Study optimizes insurance and investment strategies for risk-averse insurers under ambiguity.
problem Optimizing insurance and investment strategies for risk-averse insurers under ambiguity.
method Solves a coupled FBSDE to derive optimal strategies and value function.
result Optimal consumption, investment, and reinsurance strategies influenced by risk aversion and EIS.
Study portfolio optimization with transaction costs and recursive preferences.
problem Optimizing portfolios under transaction costs and recursive preferences.
method Recursive preferences, transaction costs, and Merton investment-consumption problem.
result Characterized all parameter combinations for well-posedness of the problem.
Study dynamic Pareto-optimal allocations in multi-period economies with time-consistent risk measures.
problem Optimal allocation in multi-period pure-exchange economies with stochastic endowments and time-consistent risk measures.
method Introduced dynamic Pareto-optimal allocation processes and derived recursive and comonotone improvement theorems.
result Dynamic Pareto-optimal allocation processes can be constructed recursively and are comonotone.
Stochastic discount factor (SDF) processes in dynamic economies admit a permanent-transitory decomposition in which the permanent component characterizes pricing over long investment horizons. This paper introduces an empirical framework to analyze the permanent-transitory decomposition of SDF processes. Specifically, …
Novel framework for teaching complexity in machine teaching models.
problem Understanding and comparing teaching models in batch and sequential settings.
method Developed a novel framework using preference functions to capture teaching complexity.
result Identified preference functions leading to linear teaching complexity in sequential models.
Algorithmic machine teaching studies the interaction between a teacher and a learner where the teacher selects labeled examples aiming at teaching a target hypothesis. In a quest to lower teaching complexity and to achieve more natural teacher-learner interactions, several teaching models and complexity measures have b…
CEFOL uses deep learning for dynamic programming with recursive utility.
problem Challenges in solving dynamic programming problems with recursive utility.
method Introduces a separate neural network for certainty equivalent, uses first-order optimality conditions to learn value and policy functions.
result CEFOL achieves high accuracy in learning value and policy functions, matching VFI benchmarks.
Proposes a new framework for resource-limited recommendation.
problem Resource constraints affect user choices in recommendation tasks.
method Interest-behavior multiplicative network with MRRNNs and resource-limited branch.
result Framework effectively predicts user interactions considering resource limitations.
Study many-player investment-consumption games with power FPPs, finding market-risk preference affects consumption.
problem Investment and consumption optimization in a mean field competition setting.
method Solve many-player and mean field games using power FPPs, providing closed-form solutions.
result Market-risk relative consumption preference affects agent's consumption decisions.
Extends wealth tax neutrality framework to stochastic volatility and non-homothetic preferences.
problem Ensuring wealth taxes are neutral under various economic conditions.
method Extended Frøseth's neutrality framework to stochastic volatility and non-homothetic preferences, identified four channels of non-neutrality, and applied the framework to global minimum wealth taxes.
result Non-uniform assessment, general equilibrium effects, progressive thresholds, and endogenous labour supply can cause non-neutrality under CRRA preferences.
Recursive neural networks have widely been used by researchers to handle applications with recursively or hierarchically structured data. However, embedded control flow deep learning frameworks such as TensorFlow, Theano, Caffe2, and MXNet fail to efficiently represent and execute such neural networks, due to lack of s…
Standard sequential generation methods assume a pre-specified generation order, such as text generation methods which generate words from left to right. In this work, we propose a framework for training models of text generation that operate in non-monotonic orders; the model directly learns good orders, without any ad…
Paper defines Farey Recursive Functions and explores their properties.
problem Understanding recursive functions on rationals.
method Defined and studied Farey Recursive Functions using Farey graph.
result Farey Recursive Functions naturally connect to 2-bridge knots and links.
The paper explores generalizations of Mirzakhani's recursion and computes volumes for physical gravity models.
problem Computing volumes for physical gravity models.
method Topological recursion and physical two-dimensional gravity models.
result Derivation of Virasoro constraints and cut-and-join equations for generalized Mirzakhani's recursions.
Study optimal consumption and investment strategies with leverage constraints using Epstein-Zin utility.
problem Optimal portfolio choice under leverage constraints and Epstein-Zin utility.
method Established viscosity solution to HJB equation, demonstrated smoothness, characterized optimal strategies, derived explicit solutions.
result Explicit solutions for optimal consumption and investment strategies under leverage constraints.
Tab-TRM uses recursive model for insurance pricing on tabular data.
problem Insurance pricing on tabular data.
method Adapts recursive latent reasoning to insurance modeling using a compact, parameter-efficient network.
result Improves insurance pricing accuracy using iterative refinement of latent tokens.
New method decomposes profits and losses continuously, avoiding discrete reporting issues.
problem Analyzing profits and losses at discrete dates ignores detailed paths.
method Constructs a large class of continuous-time decompositions using extended Itô's formula.
result Identifies a preferred decomposition from exactness, symmetry, and normalization axioms.
New recursion formula for non-orientable surfaces resolves divergences.
problem Computing volumes of moduli spaces for non-orientable surfaces.
method Generalization of Mirzakhani's recursion to non-orientable surfaces, handling divergences with integral kernels.
result Regularized volumes can be computed with a cutoff on crosscap size.
Harer and Zagier proved a recursion to enumerate gluings of a 2d-gon that result in an orientable genus g surface, in their work on Euler characteristics of moduli spaces of curves. Analogous results have been discovered for other enumerative problems, so it is natural to pose the following question: how large is t…
This paper studies recursive ensembles driven by Fibonacci updates, improving learning dynamics.
problem Improving learning dynamics in recursive ensemble learning.
method Develops second-order recursive architectures with Fibonacci-type update flows.
result Establishes global convergence conditions and generalization bounds for recursive ensembles.
The article improves prediction by aggregating Kalman recursions online.
problem Improving expert aggregation in prediction models.
method Using exponential weights and state-space models to aggregate Kalman recursions.
result New algorithms outperform existing methods in Kalman recursion expert aggregation.
Solves a recursion for Gromov-Witten invariants of the unknot.
problem Determining Gromov-Witten invariants for a specific Lagrangian brane.
method Uses a skein-theoretic recursion and geometric solutions.
result Solves the recursion to find the expected hook-content formula.
New recursion found for hyperbolic sphere volumes.
problem Volume calculation of hyperbolic sphere moduli spaces.
method Proved a non-linear recursive relation.
result Generalized Zograf's result for conical points and geodesic boundaries.
This work generalizes a formula linking Seiberg-Witten prepotential and topological recursion.
problem Analyzing the relationship between Seiberg-Witten curves and topological recursion.
method Analytical approach using Seiberg-Witten family of curves.
result A generalized formula relating Seiberg-Witten prepotential to the genus zero part of topological recursion on a Seiberg-Witten curve.
LASER compresses recursive model activations by exploiting their low-dimensional structure.
problem Understanding and optimizing the geometric structure of recursive reasoning trajectories.
method Dynamic low-rank basis tracking via matrix-free subspace tracking with a fidelity-triggered reset mechanism.
result Recursive activations occupy a linear, low-dimensional subspace that can be compressed efficiently.
We describe a method for recursively calculating Gromov-Witten invariants of all blowups of the projective plane. This recursive formula is different from the recursive formulas due to Göttsche and Pandharipande in the zero genus case, and Caporaso and Harris in the case of no blowups. We use tropical curves and a recu…
Topological recursion recovers a specific partition function for colored knots.
problem Recovering the extended Ooguri-Vafa partition function for colored HOMFLY-PT polynomials of torus knots.
method Applying topological recursion to the spectral curve of colored HOMFLY-PT polynomials of torus knots.
result Topological recursion reproduces the n-point functions of the extended Ooguri-Vafa partition function.
We derive the Do and Norbury recursion formula for the one-loop mean of an irregular spectral curve from a variant of replica method by Brezín and Hikami. We express this recursion in special times in which all terms W1(g) of the genus expansion of the one-loop mean are polynomials. We find a generalization of th…
This paper concerns the recursive utility maximization problem under partial information. We first transform our problem under partial information into the one under full information. When the generator of the recursive utility is concave, we adopt the variational formulation of the recursive utility which leads to a s…
Study on inventory management under uncertainty using smooth ambiguity preference.
problem Managing inventory under Knightian uncertainty with smooth ambiguity preference.
method Demonstrates continuous-time smooth ambiguity as the infinitesimal limit of Kalman-Bucy filtering with recursive robust utility. Solves forward-backward stochastic differential equations with quadratic growth to determine cost function. Derives value function and optimal control policy using variational inequalities and viscosity solutions. Transforms problem into two-dimensional singular control.
result Ambiguity drives decision-makers to act earlier, reducing the continuation region.
We derive a recursion relation for hyperbolic string vertices and apply it to string field theory.
problem Deriving a recursion relation for hyperbolic string vertices and its implications for string field theory.
method Using systolic volumes and a modified Mirzakhani's recursion, we construct a higher-order vertex determination for hyperbolic string field theory.
result The higher order vertices in hyperbolic string field theory are determined by the cubic vertex iteratively for any background.
Benchmarking recursive collapse claims with a new framework under false-positive control.
problem Evaluating recursive systems for failure patterns and warning claims.
method Developed Loopzero framework for testing recursive failures, specified claim boundaries in Lean, evaluated under FP constraint, and compared with standard detectors.
result No standard detectors or Loopzero's pre-registered quantile detector achieved the required operating point under the false-positive contract.
SRRM improves recursive transport surrogates in the small-discrepancy regime.
problem Insufficient understanding of recursive partitioning methods' statistical behavior and resolution in the small-discrepancy regime.
method Introduced Selective Recursive Rank Matching (SRRM) to improve the resolution of Recursive Rank Matching (RRM).
result SRRM yields a higher-fidelity practical surrogate for the Wasserstein distance at moderate additional computational cost.
This paper identifies and analyzes biases in risk-adjusted index weighting methods, affecting social welfare and market fairness.
problem Biases in risk-adjusted index weighting methods lead to tracking errors and fraud in indices and ETFs.
method Characterizes and analyzes the biases and adverse effects of risk-adjusted index weighting methods.
result These biases reduce social welfare and can enable harmful arbitrage activities.
ERM uses energy-based selection to improve recursive reasoning.
problem Lack of principled inference mechanism in recursive models.
method Energy-guided Recursive Model (ERM) introduces Hopfield energies for trajectory selection.
result ERM achieves optimal solutions on various puzzles.
Study uses reinforcement learning to optimize portfolios under recursive utility.
problem Improving portfolio allocation using risk-sensitive objectives.
method Approximated certainty equivalent via Monte Carlo, trained actor-critic algorithms (PPO, A2C).
result Recursive-utility agent outperforms discounted baseline in Sharpe ratio, max drawdown, and cumulative return.
The paper studies risk-sensitive MDPs with recursive risk measures.
problem Risk-sensitive decision-making in MDPs with unbounded costs.
method Recursive application of static risk measures, Bellman equation derivation, existence of optimal policies.
result Existence of Markovian optimal policies for infinite planning horizons, contractive model for stationary optimal policy.
New recursive relation found for a specific torus knot.
problem Finding a recursive relation for a specific torus knot.
method Extending colored Jones polynomials to knots in (2p+1,2) torus knot complements and examining a particular knot. result An analogous recursive relation exists for a specific (2p+1,2) torus knot. We propose a general theory for constructing functorial assignments Σ⟼ΩΣ∈E(Σ) for a large class of functors E from a certain category of bordered surfaces to a suitable target category of topological vector spaces. The construction proceeds by successive excisions of homotopy classes of embedded pai…
Recursive training of generative models can lead to model collapse, and the recursion converges to a unique limiting distribution.
problem Model collapse in recursive training of generative models
method Recursive training on their own outputs
result Recursive training converges to a unique limiting distribution
Paper presents novel online MTL methods using WRLS and OSLSSVR.
problem Online Multi-Task Learning (MTL) Regression Problems
method Develops recursive versions of WRLS and OSLSSVR for MTL.
result Achieves exact and approximate recursions with quadratic cost.
DILP improves fraud detection explainability without significant performance boost.
problem Improving fraud detection explainability in machine learning.
method Differentiable Inductive Logic Programming (DILP) for fraud detection with data curation.
result DILP provides comparable results to traditional methods but lacks significant advantage.
We study topological recursion on the irregular spectral curve xy2−xy+1=0, which produces a weighted count of dessins d'enfant. This analysis is then applied to topological recursion on the spectral curve xy2=1, which takes the place of the Airy curve x=y2 to describe asymptotic behaviour of enumerative proble…
Optimizes molecular generation for chemist preferences.
problem Models lack inherent preferences for chemist-desired structures.
method Fine-tuning with Direct Preference Optimization.
result Approach is simple, efficient, and highly effective.
We give an overview of the proof for Mirzakhani's volume recursion for the Weil-Petersson volumes of the moduli spaces of genus g hyperbolic surfaces with n labeled geodesic boundary components, and her application of this recursion to Witten's conjecture and the study of simple geodesic length spectrum growth rate…
New formula simplifies interior polynomial calculation.
problem Calculating interior polynomial efficiently.
method New recursion formula based on non-expanding sets.
result Clearer combinatorial interpretation of interior polynomial.