The paper tackles fair set-valued classification under demographic parity constraints.
problem Set-valued classification can amplify discriminatory bias, especially in multiclass settings.
method Proposes two strategies: an oracle-based method and a proxy method, both aiming to satisfy demographic parity and expected size constraints.
result Established distribution-free convergence rates and excess-risk bounds for both methods.
We reformulate data-dependent constraints to ensure they are always met with high probability.
problem Ensuring fairness and stability in machine learning models with data-dependent constraints.
method Calibrated reformulation of constraints to guarantee satisfaction with a specified probability.
result Our method guarantees that fairness constraints are met at test time with high probability.
Study shows equivalence of four risk constraints in non-concave optimization problems.
problem Investigating risk constraints in non-concave optimization for financial companies.
method Analytical solutions for four risk constraints (ES, EDS, VaR, AVaR) under non-concave optimization.
result All four risk constraints lead to the same optimal solution, differing from concave optimization.
Study optimality conditions for interval-valued optimization problems on Riemannian manifolds.
problem Optimizing interval-valued functions on Riemannian manifolds under a total order relation.
method Generalized Hukuhara directional differentiability to derive KKT-type optimality conditions.
result Derives optimality conditions for interval-valued optimization problems on Riemannian manifolds.
The paper examines smoothness of value function in consumption-investment models with borrowing constraints.
problem Investor's optimal consumption and investment under consumption-wealth utility and borrowing constraint.
method Second-order smoothness of value function, optimal consumption-investment policy in feedback form, smooth fit condition.
result The value function is second-order smooth and the constraint is binding under certain conditions.
Study risk aggregation with order constraint under unknown dependence.
problem Risk aggregation with an order constraint under uncertainty.
method Introduced DL coupling for concave order risk aggregation, generalized to tail risk measures.
result Analytical formulas for bounds on Value-at-Risk with improved accuracy.
Comonotonic allocations are restored under certain constraints, improving risk-sharing.
problem Feasibility constraints can distort optimal risk-sharing allocations.
method Identified componentwise convex-order solidity as a sufficient condition to restore comonotonic allocations.
result Componentwise convex-order solidity ensures comonotonic improvements under feasible constraints.
Optimal transport framework for density estimation with constraints.
problem Density estimation under expectation constraints.
method Minimizes Wasserstein distance subject to expected value constraints and regularization.
result Framework effectively addresses non-smooth constraints through annealing-like algorithm.
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.
Method estimates posterior model for boundary value problems with uncertain constraints.
problem Estimating posterior probability model for stochastic boundary value problems with uncertain constraints.
method Probabilistic learning inference using Kullback-Leibler divergence and MCMC.
result Method successfully estimates posterior probability measure with constraints.
Study examines how EU's Value at Risk constraints affect insurance oligopolies.
problem Impact of EU's Value at Risk constraints on insurance oligopolies.
method Bertrand model with profit-maximizing companies facing Value at Risk constraints.
result Value at Risk constraints can lead to monopolistic premiums or market failure.
Agent maximizes utility with pathwise constraint on portfolio value.
problem Maximizing utility with a pathwise constraint on portfolio value.
method Max-plus decomposition for supermartingales, Black-Scholes-Merton model.
result Explicit form of optimal terminal wealth and process involved.
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…
We study the portfolio selection problem of a long-run investor who is maximising the asymptotic growth rate of her expected utility. We show that, somewhat surprisingly, it is essentially not affected by introduction of a floor constraint which requires the wealth process to dominate a given benchmark at all times. We…
This paper optimizes insurance reinsurance design under solvency constraints.
problem Optimizing risk transfer from an insurance company to a reinsurer under solvency constraints.
method Martingale method to derive optimal reinsurance design maximizing terminal value of surplus.
result Optimal reinsurance designs include a combination of proportional and stop-loss protection.
Canary optimizes VaR-constrained RL problems with a conservative bound using Cantelli's inequality.
problem Optimizing reinforcement learning policies under VaR constraints in dense cost regimes.
method Employing Cantelli's inequality to create a conservative and smooth bound on VaR constraints based on moments of cost returns. Extending trust-region framework for worst-case bounds on policy improvement and constraint violation.
result Canary reliably satisfies VaR constraints with fewest violations and earliest permanent satisfaction, while maintaining reward competitiveness.
We characterize the value of swing contracts in continuous time as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation with suitable boundary conditions. The case of contracts with penalties is straightforward, and in that case only a terminal condition is needed. Conversely, the case of contracts with …
VaR-CPO optimizes VaR-constrained RL problems with conservative policy updates.
problem Optimizing VaR-constrained reinforcement learning problems.
method Combines Cantelli's inequality and trust-region framework for efficient and conservative optimization.
result Achieves zero constraint violations during training in feasible environments.
This paper is devoted to study the effects arising from imposing a value-at-risk (VaR) constraint in mean-variance portfolio selection problem for an investor who receives a stochastic cash flow which he/she must then invest in a continuous-time financial market. For simplicity, we assume that there is only one investm…
New neural network models extreme value distributions with preserved shape constraints.
problem Modeling multivariate extreme value distributions with preserved shape constraints.
method d-max-decreasing neural network architecture for non-parametric calibration and generation of MEVs.
result The proposed architecture approximates the dependence structure of MEVs at parametric rate and preserves essential shape constraints.
We show that coherent risk measures are ineffective in curbing the behaviour of investors with limited liability or excessive tail-risk seeking behaviour if the market admits statistical arbitrage opportunities which we term ρ-arbitrage for a risk measure ρ. We show how to determine analytically whether such ρ-ar…
Proposes a method to create fair ITRs that balance value and fairness.
problem Fairness issues in ITRs that can lead to unfair advantages or disadvantages.
method Optimal transport theory to transform optimal ITRs into fair ITRs.
result Established a theoretical upper bound on value loss for improved trade-off ITRs.
Dynamic risk constraints help limit risky behavior in financial portfolios.
problem Static risk measures fail to control tail-risk-seeking traders.
method Introduces dynamic risk constraints applied throughout the trading horizon.
result Dynamic risk constraints can effectively limit risky behavior in portfolios.
New RL algorithm learns good actions from offline data, reducing uncertainty and divergence.
problem Limited applicability of current RL algorithms in real-world settings due to high costs of exploration.
method Proposes an algorithm for batch RL using a fixed offline dataset, with penalties for policy and value constraints.
result Compared favorably to state-of-the-art methods on 32 continuous-action benchmarks.
Study a continuous portfolio optimization with a new CVaR-like constraint using martingale approach.
problem Optimizing a portfolio under a new CVaR-like constraint that is not compatible with traditional methods.
method Follows a martingale approach in a complete market setting, solving a convex constrained minimization problem.
result Obtains a tractable and interpretable characterization of the optimal strategy.
Optimizes multi-period portfolios with tail-risk constraints using neural networks.
problem Maximizing expected return while managing tail-risk constraints over multiple periods.
method Recurrent neural network approach to approximate optimal policy.
result Validated in financial and insurance models, capturing long-term risk dynamics.
Study S-shaped utility maximization with VaR constraint and unobservable drift.
problem Maximizing utility with a Value at Risk (VaR) constraint and unknown drift.
method Bayesian filter, concavification principle, change of measure, semi-closed integral representation, algorithms (Lagrange, simulation, deep neural network).
result Critical wealth level determining solution feasibility and optimal solution existence.
SAA method solves insurance portfolio optimization with CVaR constraints.
problem Optimal allocation under CVaR constraint in insurance.
method Sample Average Approximation (SAA) method applied to CVaR constrained portfolio optimization.
result Convergence of SAA method and solution uniqueness proved under mild assumptions.
Paper studies optimal investing for retirees with risk constraints.
problem Retirees' longevity and living standard risks in a fluctuating market.
method Formulated as a portfolio choice problem under time-varying risk capacity constraint. Derived optimal investment strategy using differential equations. Demonstrated endogenous spending measure and active investment strategy.
result Time-varying risk capacity constraint impacts asset allocation in retirement.
Discrete Lagrange problems solved with Lie group constraints.
problem Solving discrete Lagrange problems with Lie group constraints.
method Proving critical sections are solutions of unconstrained variational problems, applying Noether theory and multisymplectic forms.
result Critical sections of discrete Lagrange problems are solutions of unconstrained variational problems.
Investor optimizes investment and consumption under uncertain market conditions with constraints.
problem Investor optimizes investment and consumption in a stochastic environment with model uncertainty and constraints.
method Robust control problem solved using stochastic Hamilton-Jacobi-Bellman-Isaacs equations, backward stochastic differential equations, and bounded mean oscillation martingale theory.
result Investor incurs utility loss when ignoring model uncertainty, and constraints impact optimal strategy and value function.
Proves well-posedness for Einstein equations with totally geodesic timelike boundary condition.
problem Initial boundary value problem for Einstein equations with specific geometric boundary condition.
method ADM system, parallelly propagated orthonormal frame, modified evolution equations, hyperbolic systems, constraints propagation.
result First well-posedness result for Einstein equations with totally geodesic timelike boundary condition.
Paper doubles Hessian estimates for special Lagrangian equation with constraints.
problem Estimating Hessian for special Lagrangian equation under general phase constraints.
method Doubling argument, Alexandrov-type theorems.
result Established Hessian estimates for special Lagrangian equation.
The objective in a traditional reinforcement learning (RL) problem is to find a policy that optimizes the expected value of a performance metric such as the infinite-horizon cumulative discounted or long-run average cost/reward. In practice, optimizing the expected value alone may not be satisfactory, in that it may be…
Autonomous cyber-physical agents and systems play an increasingly large role in our lives. To ensure that agents behave in ways aligned with the values of the societies in which they operate, we must develop techniques that allow these agents to not only maximize their reward in an environment, but also to learn and fo…
The majority of stylized facts of financial time series and several Value-at-Risk measures are modeled via univariate or multivariate GARCH processes. It is not rare that advanced GARCH models fail to converge for computational reasons, and a usual parsimonious approach is the GJR-GARCH model. There is a disagreement i…
Paper introduces a new kernel model for PSD-valued functions with theoretical guarantees and applications.
problem Enforcing positive semi-definiteness (PSD) in function models with good performance and theoretical guarantees.
method Kernel sum-of-squares model for PSD-valued functions, extending previous models for non-negative scalar functions.
result The model constitutes a universal approximator of PSD functions and can represent any smooth and strongly convex function.
Proposes Constrained Q-learning for reinforcement learning with constraints.
problem Optimizing multiple objectives while adhering to constraints in reinforcement learning.
method Directly restricts the action space in Q-update to learn optimal Q-function for constrained MDP.
result Improves safety and optimality in high-level decision making for autonomous driving.
MESMOC optimizes constrained multi-objective problems efficiently.
problem Constrained multi-objective optimization with expensive function evaluations.
method Max-value Entropy Search in the output space.
result MESMOC selects high-quality Pareto solutions efficiently.
Algorithm ensures privacy while strictly adhering to constraints.
problem Differential privacy with linear constraints that must be strictly followed.
method Developed an algorithm that releases a nearly-optimal solution satisfying constraints with probability 1.
result Achieved nearly optimal performance while preserving privacy and strictly adhering to constraints.
The paper solves portfolio optimization problems with risk constraints.
problem Maximizing utility while ensuring a certain wealth threshold with risk constraints.
method Derives Nash equilibria for two agents and characterizes them for more than two agents.
result Characterizes Nash equilibria for different cases of competition probabilities.
New method parameterizes solutions to linearized vacuum constraints on Einstein manifolds.
problem Parameterizing solutions to linearized vacuum constraints on Einstein manifolds.
method Parameterize solutions using unconstrained potentials and shield linearized gravitational fields.
result Showed how to shield linearized gravitational fields without TT gauge for any value of cosmological constant.
This paper optimizes dividend payout rates with a drawdown constraint in a stochastic model.
problem Optimizing dividend payout rates while avoiding drawdowns in a stochastic model.
method Solving a path-dependent stochastic control problem using Hamilton-Jacobi-Bellman equations and PDE methods.
result Explicit characterization of an optimal feedback control strategy, including two free boundaries and the running maximum surplus process.
This paper investigates optimal consumption in the stochastic Ramsey problem with the Cobb-Douglas production function. Contrary to prior studies, we allow for general consumption processes, without any a priori boundedness constraint. A non-standard stochastic differential equation, with neither Lipschitz continuity n…
We consider the problem of utility maximization for small traders on incomplete financial markets. As opposed to most of the papers dealing with this subject, the investors' trading strategies we allow underly constraints described by closed, but not necessarily convex, sets. The final wealths obtained by trading under…
We consider a utility-maximization problem in a general semimartingale financial model, subject to constraints on the number of shares held in each risky asset. These constraints are modeled by predictable convex-set-valued processes whose values do not necessarily contain the origin; that is, it may be inadmissible fo…
DC3 uses deep learning to solve hard-constrained optimization problems efficiently.
problem Hard constraints in optimization problems make classical solvers slow and infeasible.
method DC3 employs a differentiable procedure to enforce feasibility and unrolls corrections for inequality constraints.
result DC3 achieves near-optimal solutions while maintaining feasibility in both synthetic and real-world tasks.
Study optimal stopping times under regime-switching models with constraints.
problem Optimal stopping times for discounted payoffs on a regime-switching geometric Brownian motion.
method Solve variational inequality to find value functions and optimal thresholds.
result Existence and expressions of optimal stopping times under specific conditions.