The paper solves MMV and MV problems with random coefficients and finds shared optimal strategies.
problem Optimal trading strategies with random market coefficients.
method Backward stochastic differential equations (BSDEs) to find optimal strategies.
result MMV and MV problems share the same optimal portfolio and value under random coefficients.
Study optimal consumption and investment strategies with constraints in a market with random coefficients.
problem Optimal consumption and investment strategies with constraints in a regime switching market with random coefficients.
method Explicit optimal strategies provided via solutions to new BSDE systems.
result Solving new BSDEs to find optimal values and strategies.
Study optimal portfolios for many players in a market model with random coefficients.
problem Optimal portfolio selection for many players under relative performance criteria in a market model with random coefficients.
method Game theory and stochastic optimal control, focusing on CARA and CRRA risk preferences, and extending to continuum of players.
result Existence of forward Nash equilibrium and mean field equilibrium for the n-agent game and corresponding mean field stochastic optimal control problem.
Improved portfolio optimization using Kendall-like correlation coefficients.
problem Accurate estimation of eigenvectors in data-poor regimes for portfolio optimization.
method Developed generalized correlation coefficients based on Kendall's rank correlation.
result Markowitz portfolios with lower out-of-sample risk using these coefficients.
We consider the problem of constructing a reduced-rank regression model whose coefficient parameter is represented as a singular value decomposition with sparse singular vectors. The traditional estimation procedure for the coefficient parameter often fails when the true rank of the parameter is high. To overcome this …
The nullspace and regularization impact high-dimensional linear regression interpretability.
problem Interpreting high-dimensional linear regression coefficients in complex data.
method Optimization formulation to compare coefficients and physical knowledge.
result Regularization and z-scoring choices affect interpretability and true coefficient closeness.
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…
The group lasso is a penalized regression method, used in regression problems where the covariates are partitioned into groups to promote sparsity at the group level. Existing methods for finding the group lasso estimator either use gradient projection methods to update the entire coefficient vector simultaneously at e…
The paper solves a complex control problem with stochastic elements and switching conditions.
problem Non-homogeneous stochastic LQ control with regime switching and random coefficients.
method Explicit optimal control and value obtained through two systems of backward stochastic differential equations (BSDEs). Existence and uniqueness of solutions proved using BMO martingales and contraction mapping method.
result Explicit optimal state feedback control and optimal value derived for the problem.
This work addresses unstable MeanFlow training by optimizing a coefficient in the loss function.
problem Unstable training of MeanFlow models with non-decreasing loss and unbounded gradient variance.
method Established a theory attributing the instability to misuse of the conditional velocity field, derived the optimal coefficient, and showed practical realizations.
result Optimal coefficient yields up to 54% improvement in sample quality and monotone FID trend.
Optimizes dividend payouts with fixed costs and regime switching.
problem Maximizing dividends with fixed transaction costs and regime switching.
method Identifies optimal dividend strategy as a two-barrier impulsive strategy.
result Explicit determination of optimal strategy for various drift and volatility scenarios.
Study optimal investment-reinsurance strategy for insurers under random coefficients and jumps.
problem Optimal investment-reinsurance strategy for insurers with random coefficients and jumps.
method Solves backward stochastic differential equations with jumps under a convex cone constraint.
result Optimal strategy and value remain the same even with random coefficients and jumps.
We investigate the ergodic problem of growth-rate maximization under a class of risk constraints in the context of incomplete, Itô-process models of financial markets with random ergodic coefficients. Including {\em value-at-risk} (VaR), {\em tail-value-at-risk} (TVaR), and {\em limited expected loss} (LEL), these cons…
This paper introduces a new data-driven methodology for estimating sparse covariance matrices of the random coefficients in logit mixture models. Researchers typically specify covariance matrices in logit mixture models under one of two extreme assumptions: either an unrestricted full covariance matrix (allowing correl…
New method finds optimal hyperparameters for multiple tasks and criteria.
problem Finding optimal hyperparameters for multiple tasks and criteria.
method Multi-Task Multi Criteria (MTMC) method that provides Pareto-optimal solutions.
result The method selects optimal hyperparameters based on given criteria significance coefficients.
New method optimizes tail dependence coefficient estimation.
problem Estimating tail dependence in nonparametric data.
method Optimal threshold selection combining mean squared error and copula estimation.
result Improved accuracy in tail dependence coefficient estimation.
Optimal B-robust estimate is constructed for multidimensional parameter in drift coefficient of diffusion type process with small noise. Optimal mean-variance robust (optimal V -robust) trading strategy is find to hedge in mean-variance sense the contingent claim in incomplete financial market with arbitrary informatio…
This paper concerns the recursive utility maximization problem. We assume that the coefficients of the wealth equation and the recursive utility are concave. Then some interesting and important cases with nonlinear and nonsmooth coefficients satisfy our assumption. After given an equivalent backward formulation of our …
MeanFlow training is unstable due to misusing conditional velocity, leading to variance issues.
problem Unstable training of MeanFlow due to variance problems.
method Theoretical analysis and derivation of optimal coefficient in closed form.
result The optimal coefficient in MeanFlow training minimizes variance but not necessarily quality.
Develops an algorithm to find the best subset of points for maximizing the coefficient of determination.
problem Finding the optimal subset of points for maximizing the coefficient of determination in robust correlation analysis.
method The extit{quadratic sweep} method, which involves projecting points into \(\mathbb{R}^5\) and iterating over linearly separable \(k\)-subsets.
result The method optimally finds the best subset of points for maximizing the coefficient of determination without error over several million trials up to \(n=30\).
A new method solves complex control problems with random coefficients.
problem Solving LQ McKean-Vlasov control problems with random coefficients.
method Decomposes the problem into two decoupled stochastic optimal control problems.
result The sum of optimal controls of auxiliary problems equals the original problem's optimal control.
New method for MTL with varying sparsity patterns across tasks.
problem Jointly training multiple linear models with differing sparsity patterns.
method Mixed-integer programming formulation and scalable algorithms.
result Our methods leverage shared support information to improve variable selection.
Improves functional linear regression with shape transfer learning.
problem Data scarcity in functional linear models.
method Shape-based transfer learning from auxiliary to target domains.
result Enhances robustness and generalizability of functional linear models.
Improved SVRG with a coefficient reduces training loss in deep learning.
problem Demonstrating SVRG's effectiveness in deep learning.
method Introduced a multiplicative coefficient α to control SVRG's variance reduction strength and decay it linearly.
result α-SVRG consistently reduces training loss compared to baseline and standard SVRG across various model architectures and datasets.
Optimizes maps with controlled distortion for geometric tasks.
problem Free-boundary diffeomorphism optimization in geometric modeling.
method Least-squares quasiconformal (LSQC) operator and Spectral Beltrami Network (SBN).
result LSQC minimizer well-posed under mild conditions, stable under mesh refinement.
We study singular stochastic control of a two dimensional stochastic differential equation, where the first component is linear with random and unbounded coefficients. We derive existence of an optimal relaxed control and necessary conditions for optimality in the form of a mixed relaxed-singular maximum principle in a…
The paper introduces a machine learning method to forecast market direction using efficient frontier coefficients.
problem Improving asset return estimation for portfolio optimization.
method Monthly directional market forecast using an online decision tree trained on efficient frontier coefficients.
result The method outperforms baseline portfolios and other feature sets.
New method improves DAG learning by using large coefficients for higher-order terms.
problem Recovering DAG structures from observational data is challenging due to combinatorial optimization.
method Proposes truncated matrix power iteration to approximate DAG constraints efficiently.
result Empirically outperforms previous methods by a factor of 3 or more in structural Hamming distance.
We consider the dictionary learning problem, where the aim is to model the given data as a linear combination of a few columns of a matrix known as a dictionary, where the sparse weights forming the linear combination are known as coefficients. Since the dictionary and coefficients, parameterizing the linear model are …
We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes with respect to the common noise filtration. Semi closed-loop strategies are intro…
New method synthesizes and analyzes probability measures using entropy-regularized optimal transport.
problem Synthesize and analyze probability measures with entropy-regularized optimal transport.
method Entropy-regularized Wasserstein-2 cost and Sinkhorn divergence for synthesis and analysis.
result Computed barycentric coefficients and their stability for classification of corrupted point cloud data.
A new asset allocation model uses Markov states from clustered efficient frontier coefficients.
problem Characterizing market regimes using efficient frontiers for better asset allocation.
method Hierarchical clustering of monthly efficient frontier coefficients to define states, then a Markov process on these states for portfolio optimization.
result The model significantly outperforms benchmark portfolios empirically.
We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic coefficients driven by a diffusion process. We assume that an agent makes consumption and investment decisions based on CRRA utility functions. The dynamical programming approach leads to an investigation of t…
Paper proposes methods for transfer learning with random coefficient ridge regression.
problem Estimation and prediction in high-dimensional settings with related models.
method Two estimators using weighted sums of ridge estimates from target and source models.
result Explicit expression of estimation and prediction risks derived using random matrix theory.
Optimal convex loss function improves regression coefficient estimation.
problem Asymptotic variance improvement in linear regression estimation.
method Score matching extension for log-concave projection.
result Semiparametric estimator attains minimal asymptotic covariance.
This work studies the contraction coefficients of Schrödinger bridge problems in linear systems.
problem Optimally controlling the evolution of a system's state density over time.
method Analyzes and improves the convergence rates of dynamic Schrödinger systems via geometric and control-theoretic interpretations.
result New insights into improving computation of worst-case contraction coefficients by preconditioning.
The paper tackles online resource allocation with uncertain coefficients and chance constraints.
problem Online stochastic resource allocation problem with chance constraints.
method Linearization and primal-dual algorithms with heuristic corrections.
result Optimality gap and constraint violation are on the order of √n.
We investigate the possible drawbacks of employing the standard Pearson estimator to measure correlation coefficients between financial stocks in the presence of non-stationary behavior, and we provide empirical evidence against the well-established common knowledge that using longer price time series provides better, …
We consider the generic regularized optimization problem β^(λ)=argminβL(y,Xβ)+λJ(β). Efron, Hastie, Johnstone and Tibshirani [Ann. Statist. 32 (2004) 407--499] have shown that for the LASSO--that is, if L is squared error loss and J(β)=∥β∥1 is the ℓ1 norm of β--the opti…
GenMod uses generative models to approximate high-dimensional PDE solutions with limited evaluations.
problem Quantifying uncertainty in high-dimensional PDE systems with random parameters.
method Develops a method using generative models to approximate polynomial chaos coefficients in underdetermined systems.
result The method outperforms sparsity-promoting methods in approximating PDE solutions with limited evaluations.
Adaptive transfer learning model for varying mechanisms across domains.
problem Improving inference in a target domain by leveraging related source domains with varying mechanisms.
method Semi-parametric domain-varying coefficient model (DVCM) for structured transfer learning.
result Minimax rate-optimal adaptive transfer learning estimator with provable negative transfer safeguards.
Study optimal investment and reinsurance strategy for insurers under random coefficients.
problem Optimal mean-variance investment-reinsurance problem for insurers under Cramér-Lundberg model with random coefficients.
method Reduced to a constrained stochastic linear-quadratic control problem with jumps, solved using BSDE techniques and SREs.
result Explicit efficient investment-reinsurance strategy and mean-variance frontier.
Proposes a new consumption strategy based on martingale principles.
problem Optimizing consumption based on investment strategies without risk preferences.
method Introduces martingale consumption as a consumption pattern that adjusts to expected future consumption.
result Identifies explicit solutions in deterministic models and establishes uniqueness in general cases.
The speed of convergence of the Expectation Maximization (EM) algorithm for Gaussian mixture model fitting is known to be dependent on the amount of overlap among the mixture components. In this paper, we study the impact of mixing coefficients on the convergence of EM. We show that when the mixture components exhibit …
New complexity measure for interactive learning reduces regret to near-optimal levels.
problem Challenges in sample-efficient, adaptive learning algorithms for interactive decision making.
method Introduces the Decision-Estimation Coefficient and the Estimation-to-Decisions (E2D) principle.
result Unified algorithm design principle E2D achieves optimal sample-efficient learning.
In this paper, we investigate an optimal investment and consumption problem for an investor who trades in a Black--Scholes financial market with stochastic coefficients driven by a non-Gaussian Ornstein--Uhlenbeck process. We assume that an agent makes investment and consumption decisions based on a power utility funct…
We propose a semismooth Newton algorithm for pathwise optimization (SNAP) for the LASSO and Enet in sparse, high-dimensional linear regression. SNAP is derived from a suitable formulation of the KKT conditions based on Newton derivatives. It solves the semismooth KKT equations efficiently by actively and continuously s…
We analyze how uncertainty in models affects optimization outcomes using Wasserstein distances.
problem Sensitivity of optimization problems to model uncertainty.
method Non-parametric approach using Wasserstein balls to capture uncertainty, providing explicit corrections for value function and optimizer.
result Explicit formulae for first-order corrections to value function and optimizer.