The paper addresses utility maximization in markets with transaction costs, focusing on stability and optimal dual processes.
problem Utility maximization in markets with proportional transaction costs.
method Analysis of primal and dual value functions, study of optimal dual process, construction of limiting ODP.
result The optimal dual process defines a shadow price in the limiting market.
Study optimal dividends in dual risk model with stochastic interest rate.
problem Optimal dividend strategy in dual risk model with stochastic interest rate.
method Geometric Brownian motion or exponential Lévy process for discounting factor.
result Closed form solutions can be obtained for optimal dividends.
The paper improves Gaussian process models for efficient batch optimization.
problem Poor scaling and optimization loop issues in Gaussian process models.
method Dual GP parameterization for linear scaling and non-Gaussian likelihood updates.
result Extends sparse models to greedy batch fantasizing acquisition functions.
Study optimal consumption with relaxed benchmarks and drawdown constraints.
problem Optimal consumption under relaxed benchmark tracking and consumption drawdown constraint.
method Transformed stochastic control problem into regular control problem with state-control constraints, then solved using dual transform and optimal consumption behavior.
result Closed-form solution for optimal investment and consumption in feedback form.
The paper simplifies utility maximization problems using dynamic convex duality.
problem Constrained utility maximization problems.
method Formulating primal and dual problems, using FBSDEs, and characterizing optimal controls.
result Explicit dynamic characterization of optimal controls and wealth processes.
Study optimal dividends in dual risk model under extreme parameter conditions.
problem Optimal dividends in a dual risk model with extreme parameters.
method Asymptotic analysis of optimal control problem.
result Insights into optimal strategies and values under extreme parameter conditions.
Study optimizes dividend strategies for risk processes with Lévy jumps.
problem Optimizing dividend payments in risk processes with Lévy jumps.
method Analyzes spectrally positive and negative Lévy processes, using scale functions.
result Periodic barrier strategy is optimal for spectrally negative Lévy processes with completely monotone Lévy density.
APDO optimizes CMDPs with off-policy dual updates for faster convergence.
problem Learning policies that maximize long-term reward while satisfying safety constraints.
method Accelerated Primal-Dual Optimization (APDO) incorporating off-policy dual updates.
result APDO achieves better sample efficiency and faster convergence than existing methods.
Neural model accelerates SDDP for stochastic optimization.
problem Exponential complexity of SDDP limits its applicability to low-dimensional problems.
method Trainable neural model maps problem instances to a low-dimensional piecewise linear value function.
result ν-SDDP significantly reduces problem solving cost without sacrificing solution quality.
New method improves image and signal processing with nonconvex rank surrogates and dual momentum.
problem Optimizing nonconvex rank minimization problems in image processing.
method Proposes a novel nonconvex rank surrogate, uses ADMM with dual momentum trick.
result Effective in image and signal processing applications, outperforming state-of-the-art methods.
New algorithm reduces big data processing time by sketching and random projection.
problem Efficiently processing large and high-dimensional data sets.
method Developed a new algorithm combining sketching and dual random projection, using preconditioned conjugate gradient.
result The algorithm can recover the optimum of the original problem up to arbitrary precision with a logarithmic number of small-scale solver calls.
We study the stochastic control problem of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is to derive the optimal insurance strategy which allows "lowering" the level of the…
The dual representation of the martingale optimal transport problem in the Skorokhod space of multi dimensional cadlag processes is proved. The dual is a minimization problem with constraints involving stochastic integrals and is similar to the Kantorovich dual of the standard optimal transport problem. The constraints…
A method to improve sequential learning by keeping past data errors in check.
problem Challenges in sequential learning with Gaussian processes due to accumulating errors.
method Memory-based dual sparse variational Gaussian processes.
result Improves accuracy in inference and learning for various applications.
In this paper we study the optimal dividend problem for a company whose surplus process evolves as a spectrally positive Levy process. This model including the dual model of the classical risk model and the dual model with diffusion as special cases. We assume that dividends are paid to the shareholders according to ad…
We revisit the dividend payment problem in the dual model of Avanzi et al. ([2], [1], and [3]). Using the fluctuation theory of spectrally positive Lévy processes, we give a short exposition in which we show the optimality of barrier strategies for all such Lévy processes. Moreover, we characterize the optimal barrier …
Optimizes hybrid dividend strategies in dual models with periodic and continuous payments.
problem Determining the best dividend strategy in a dual model with periodic and continuous payments.
method Generalizes results from a Brownian model to a dual (spectrally positive Lévy) model, using the scale function.
result The optimal strategy is of the hybrid-barrier type and can be expressed using the scale function.
A new kernel for probability measures based on optimal transport.
problem Efficiently comparing and modeling distributions.
method Kernel over probability measures using regularized optimal transport and Hilbertian embedding.
result The proposed kernel enables Gaussian process modeling on distributions with theoretical and computational advantages.
New algorithm selects robust martingale for optimal stopping problems.
problem Optimal stopping problems in stochastic processes.
method Randomized dual martingale minimization algorithm.
result Efficiently selects Doob martingale as close as possible.
This paper deals with numerical solutions of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is to derive the optimal insurance strategy which allows "lowering" the level of t…
The paper optimizes utility for switching models using Lévy processes.
problem Maximizing HARA utilities in Lévy switching models.
method Dual method, f-divergence minimal martingale measures, Hellinger and Kulback-Leibler processes.
result Expressions for optimal strategies and maximal expected utilities.
We solve optimal consumption in a market with bounded risk.
problem Optimal consumption in a semimartingale market with bounded risk.
method Use supermartingale deflators to prove strong duality.
result Strong duality and complete characterisation of optimal consumption.
Paper studies optimal tracking portfolio in mean field game of large fund competition.
problem Optimal tracking portfolio in large fund competition with relative performance benchmark.
method Formulated mean field game problem, established existence of mean field equilibrium using PDE approach, constructed approximate Nash equilibrium.
result Existence of mean field equilibrium and consistency condition verified.
Unified framework for entropy-regularized reinforcement learning in MDPs.
problem Entropy-regularized reinforcement learning in Markov decision processes.
method Extending linear programming to accommodate convex regularization functions.
result Using conditional entropy as regularization yields a dual problem similar to Bellman equations.
Study optimal dividend strategy with time of ruin constraint for financial firms.
problem Optimal dividend strategy with time of ruin constraint for spectrally one-sided Lévy risk models.
method Introduced a longevity feature to the classical optimal dividend problem, extended results to one-sided Lévy risk models, and characterized the solution using dual problems.
result Characterized the solution to the constrained optimal dividend problem for spectrally one-sided Lévy processes.
Investment problem solved with value function regularity and PDE analysis.
problem Optimal investing with utility functions on the real line.
method Regularity of dynamic value functions, decomposition terms, backward stochastic PDE.
result Value function satisfies backward stochastic PDE in complete markets.
Algorithm optimizes constrained reinforcement learning with dual variables.
problem Minimizing convex functional subject to convex constraint in large state spaces.
method VPDPO algorithm using Lagrangian and Fenchel duality.
result Achieves sublinear regret and constraint violation, globally optimal policy.
We study the utility maximization problem for power utility random fields in a semimartingale financial market, with and without intermediate consumption. The notion of an opportunity process is introduced as a reduced form of the value process of the resulting stochastic control problem. We show how the opportunity pr…
Improves SDCA convergence for convex objectives with linear constraints.
problem Minimizing convex objectives with linear constraints under gradient-Lipschitz assumption failure.
method Shifted Stochastic Dual Coordinate Ascent (SDCA) under smoothness assumption.
result Obtains linear convergence rate for Poisson regression and Hawkes process objectives.
This paper solves a utility maximization problem under utility-based shortfall risk constraint, by proposing an approach using Lagrange multiplier and convex duality. Under mild conditions on the asymptotic elasticity of the utility function and the loss function, we find an optimal wealth process for the constrained p…
Develops a regression approach for solving MDPs with general state and action spaces.
problem Solving MDPs with large or infinite state and action spaces.
method Regression-based primal-dual martingale approach.
result Tight upper and lower approximations of value functions and optimal policies.
New SPD methods improve online policy estimation in MDPs with reduced storage and complexity.
problem Online estimation of optimal policies in Markov decision processes (MDPs).
method Stochastic Primal-Dual (SPD) methods that update few coordinates of value and policy estimates.
result SPD methods find absolute-ε-optimal policies with high probability using a specified number of iterations/samples. Fast pricing of American-style options has been a difficult problem since it was first introduced to financial markets in 1970s, especially when the underlying stocks' prices follow some jump-diffusion processes. In this paper, we propose a new algorithm to generate tight upper bounds on the Bermudan option price witho…
Dual supervised learning improves model performance for dual tasks.
problem Separate training of dual tasks misses probabilistic connections.
method Simultaneous training of dual tasks exploiting probabilistic correlations.
result Dual supervised learning improves practical performance across various applications.
Paper develops efficient estimator for Hawkes processes using representer theorem.
problem Estimating latent triggering kernels for Hawkes processes from event sequences.
method Penalized least squares minimization in RKHS framework.
result Efficient estimator with competitive accuracy and improved computational efficiency.
New method solves saddle-point problems faster than existing methods.
problem Large-scale saddle-point problems in optimization.
method Sequential subspace optimization with proximal regularization.
result Significantly better convergence compared to first-order methods.
The paper solves a finance problem using stochastic equations.
problem Risk minimization with portfolio constraints in financial markets.
method Uses Forward and Backward Stochastic Differential Equations (FBSDEs) to model and solve the problem.
result Explicit representations of solutions to quadratic risk minimization problems with constraints are derived.
The paper solves a control problem using reflections to track a benchmark process.
problem Optimal consumption with a benchmark process that grows over time.
method Introduced two auxiliary state processes with reflections to transform the problem into a more tractable form.
result Established the existence of a unique classical solution to the dual PDE.
A new GAN training method using primal-dual subgradient methods.
problem Training GANs to avoid mode collapse and generate diverse samples.
method Relating GANs to convex optimization via Lagrangian perspective and primal-dual subgradient methods.
result The proposed method resolves mode collapse and generates diverse samples.
This paper studies the continuous time utility maximization problem on consumption with addictive habit formation in incomplete semimartingale markets. Introducing the set of auxiliary state processes and the modified dual space, we embed our original problem into a time-separable utility maximization problem with a sh…
MDA optimizer performs similarly to SGD+M in CV and Adam in NLP.
problem Performance degradation due to choosing the wrong optimizer.
method Modernized Dual Averaging (MDA) optimizer, inspired by dual averaging.
result MDA performs as well as SGD+M in CV and as Adam in NLP.
Improves SVGP methods for faster and more accurate Gaussian process inference.
problem Efficient non-conjugate Gaussian process inference.
method Dual parameterization of SVGP methods using site parameters.
result Faster and more accurate inference with tighter evidence lower bound.
We maximize the expected utility of terminal wealth in an incomplete market where there are cone constraints on the investor's portfolio process and the utility function is not assumed to be strictly concave or differentiable. We establish the existence of the optimal solutions to the primal and dual problems and their…
A new algorithm finds optimal solutions for constrained decision processes.
problem Optimizing state-value functions with constraints in CMDPs.
method Gradient-Aware Search (GAS) exploiting PWLC structure.
result GAS converges faster and more reliably than existing methods.
Dual ML approach predicts peak temperatures in AFSD, improving process optimization.
problem Lack of understanding between process parameters and resulting microstructure in AFSD.
method Combines supervised machine learning and physics-informed neural networks.
result Ensemble techniques like gradient boosting outperform other SML methods in predicting peak temperatures.
Study optimizes financial strategies for various options globally.
problem Optimizing financial strategies for different types of options.
method Martingale optimal transport duality for càdlàg processes.
result Existence of robust semi-static superhedging strategies.
The important application of semi-static hedging in financial markets naturally leads to the notion of quasi self-dual processes which is, for continuous semimartingales, related to symmetry properties of both their ordinary as well as their stochastic logarithms. We provide a structure result for continuous quasi self…
New algorithm for fast nonsmooth optimization with applications in image processing and machine learning.
problem Minimizing the sum of three convex functions with specific properties.
method PDDY algorithm, based on Davis-Yin splitting in a primal-dual product space.
result Sublinear and linear convergence rates in various scenarios, including strong convexity.