Optimizes neural networks' last layer with closed-form solutions.
problem Optimizing neural networks' last layer with stochastic gradient descent.
method Adapting closed-form last layer optimization for stochastic gradient descent, alternating between backbone and last layer updates.
result The method converges to optimal solutions and outperforms standard SGD and Adam in regression tasks.
Improved portfolio optimization using VaR and CVaR with NMVM models.
problem Optimizing portfolios with VaR and CVaR under NMVM distributions.
method Transformed mean-CVaR-skewness problems into quadratic optimization with closed-form solutions for NMVM models.
result Approximate closed-form expressions for VaR and CVaR of NMVM portfolios.
Develops first closed-form portfolio formula for GARCH spot assets.
problem Optimizing portfolio allocation for assets with time-varying volatility.
method Closed-form solution for CRRA utility maximization under HN-GARCH model.
result Optimal strategy is independent of asset volatility development.
This note finds closed-form solutions for mean-risk portfolios using a specific type of mixture distribution.
problem Finding optimal portfolios under mean-risk criteria for general distributions.
method Using normal mean-variance mixture (NMVM) distributions, the paper derives closed-form expressions for mean-risk frontiers by optimizing a Markowitz model with adjusted return vectors.
result Closed-form solutions for mean-risk portfolios are found for return vectors following NMVM distributions.
Neural network discovers exact solutions to QP with linear constraints.
problem Discovering exact solutions to Quadratic Programs (QP) with linear constraints using neural networks.
method Proposes a neural network modeling approach that analytically derives model parameters from problem coefficients, ensuring closed-form solutions without training.
result The closed-form NN model produces exact solutions for every critical region of the QP solution function, outperforming DNNs and commercial solvers in terms of optimality and feasibility.
We present three models of stock price with time-dependent interest rate, dividend yield, and volatility, respectively, that allow for explicit forms of the optimal exercise boundary of the finite maturity American put option. The optimal exercise boundary satisfies the nonlinear integral equation of Volterra type. We …
The paper examines optimal insurance design using Lambda-Value-at-Risk.
problem Optimal insurance design based on Lambda-Value-at-Risk.
method Analyzes optimal insurance solutions using Lambda-Value-at-Risk and closed-form expressions.
result Truncated stop-loss indemnity is optimal under certain conditions.
A large proportion of market making models derive from the seminal model of Avellaneda and Stoikov. The numerical approximation of the value function and the optimal quotes in these models remains a challenge when the number of assets is large. In this article, we propose closed-form approximations for the value functi…
Closed-form optimal portfolios for exponential utility in small/large markets.
problem Optimal portfolios maximizing exponential utility in small/large financial markets.
method Closed-form expressions for optimal portfolios in small markets, convergence to large market optimal utility, numerical procedure for general utility functions.
result Optimal utility in large markets converges to optimal utility in small markets, requiring infinite diversification.
Optimal portfolio yields a digital option payoff.
problem Portfolio optimization under generalized dual theory of choice.
method Characterized optimal solution and derived it in closed form.
result Payoff is a digital option that yields in-the-money payoff in good market scenarios.
We solve a Schrödinger bridge with a quadratic state cost, finding a closed-form solution.
problem Optimizing diffusion processes between given distributions.
method Regularized Schrödinger bridge with a quadratic state cost.
result Closed-form solution for the Markov kernel of the regularized Schrödinger bridge.
In this paper we study a class of insurance products where the policy holder has the option to insure k of its annual Operational Risk losses in a horizon of T years. This involves a choice of k out of T years in which to apply the insurance policy coverage by making claims against losses in the given year. The…
In this paper we study a utility maximization problem with both optimal control and optimal stopping in a finite time horizon. The value function can be characterized by a variational equation that involves a free boundary problem of a fully nonlinear partial differential equation. Using the dual control method, we der…
We propose Deep Closed-Form Subspace Clustering (DCFSC), a new embarrassingly simple model for subspace clustering with learning non-linear mapping. Compared with the previous deep subspace clustering (DSC) techniques, our DCFSC does not have any parameters at all for the self-expressive layer. Instead, DCFSC utilizes …
Agent optimizes perpetual contract liquidation with transaction costs and risk.
problem Optimizing perpetual contract liquidation with transaction costs and risk.
method Solving stochastic control problem for optimal trading strategy.
result Closed-form expression and approximations for optimal strategy.
Study on utility maximization with Tsallis entropy in reinforcement learning.
problem Exploring utility maximization with Tsallis entropy in reinforcement learning.
method Introducing Tsallis entropy regularizer to induce exploration, investigating specific examples, characterizing well-posedness, designing reinforcement learning algorithm.
result Characterized well-posedness and provided semi-closed-form solutions for specific examples, found distinct optimal strategies.
Closed-form relations and approximations for SE(3) derivatives for robust numerical simulations.
problem Deriving closed-form derivatives and approximations for SE(3) for robust numerical simulations.
method Avoiding block partitioning, deriving higher-order approximations for differential, first and second derivatives, Jacobian, and Hessian.
result Compact and numerically robust closed-form relations for SE(3) derivatives.
Bayes-optimal learning of deep random networks with Gaussian weights is studied.
problem Learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights.
method Closed-form expressions for Bayes-optimal test error, ridge regression, kernel and random features regression are computed.
result Optimally regularized ridge regression and kernel regression achieve Bayes-optimal performances, while logistic loss yields a near-optimal test error for classification.
Study optimal portfolios in a non-Markovian regime-switching model with random time horizon.
problem Optimal portfolio selection in a market with non-Markovian regime-switching and random time horizon.
method Formulated as a constrained stochastic linear-quadratic optimal control problem, derived closed-form expressions for optimal portfolios and efficient frontier.
result Closed-form expressions for optimal portfolios and efficient frontier derived under non-Markovian regime-switching and random time horizon.
COSMIC identifies LTV systems from large data sets efficiently.
problem Identification of discrete-time linear time-variant systems from large-scale data.
method Formulates as regularized least squares problem, develops closed-form algorithm with linear complexity.
result Achieves optimal results even with large data volumes, significantly faster than general solvers.
We revisit the task of learning a Euclidean metric from data. We approach this problem from first principles and formulate it as a surprisingly simple optimization problem. Indeed, our formulation even admits a closed form solution. This solution possesses several very attractive properties: (i) an innate geometric app…
Paper finds closed-form solutions for tontine with bequest motive.
problem Finding optimal fractional consumption rate and bequest amount under bequest motive.
method Relaxing fixed proportions assumption, introducing bequest proportion as control function.
result Closed-form solutions for fractional consumption rate, wealth, bequest amount, and proportion.
Assuming geometric Brownian motion as unaffected price process S0, Gatheral & Schied (2011) derived a strategy for optimal order execution that reacts in a sensible manner on market changes but can still be computed in closed form. Here we will investigate the robustness of this strategy with respect to misspecifica…
We deal with the efficient parallelization of Bayesian global optimization algorithms, and more specifically of those based on the expected improvement criterion and its variants. A closed form formula relying on multivariate Gaussian cumulative distribution functions is established for a generalized version of the mul…
Closed-form solutions derived for perpetual options under insider models.
problem Pricing perpetual American standard and lookback options for insiders.
method Closed-form solutions derived using progressively enlarged filtrations and optimal stopping problems.
result Optimal exercise times determined based on asset price maximum or minimum.
In this paper, we consider the Graphical Lasso (GL), a popular optimization problem for learning the sparse representations of high-dimensional datasets, which is well-known to be computationally expensive for large-scale problems. Recently, we have shown that the sparsity pattern of the optimal solution of GL is equiv…
Unified view on GP transfer learning for Bayesian optimization.
problem Improving data efficiency in Bayesian optimization with scarce data.
method Unified hierarchical GP models for transfer learning, including a novel boosted GP transfer model.
result Unified analysis and comparison of transfer learning methods for GP models.
This research reverses feature visualization in neural networks to optimize for specific feature objectives.
problem The invertibility of feature visualization in neural networks is not well understood.
method The approach involves optimizing for the feature objective that generates the input used in feature visualization, using the gradient of a specific objective function.
result A closed-form solution is found to minimize the gradient, providing an alternative view on network sensitivity.
Paper derives a simplified formula for Expected Improvement using log-transformed data.
problem Challenges in enhancing Bayesian optimization with Expected Improvement.
method Derives a closed form of Expected Improvement for Gaussian process trained on log-transformed objective.
result Provides a simplified formula for Expected Improvement.
Optimized GAN discriminator using polyharmonic interpolation.
problem Optimizing the discriminator in GANs with higher-order gradient regularization.
method Polyharmonic interpolation and variational calculus.
result The optimal discriminator is a polyharmonic radial basis function.
We consider the problem of optimal consumption of multiple goods in incomplete semimartingale markets. We formulate the dual problem and identify conditions that allow for existence and uniqueness of the solution and give a characterization of the optimal consumption strategy in terms of the dual optimizer. We illustra…
A risk-averse agent hedges her exposure to a non-tradable risk factor U using a correlated traded asset S and accounts for the impact of her trades on both factors. The effect of the agent's trades on U is referred to as cross-impact. By solving the agent's stochastic control problem, we obtain a closed-form expr…
Alternative closed-form formula for spread call option prices under log-normal models.
problem Valuation of spread call options under log-normal models.
method Developed an alternative closed-form formula for spread call option prices.
result Our formula performs better for certain range of model parameters than existing closed-form formula.
New Frank-Wolfe algorithm speeds up SVM-type multi-category learning.
problem Improving pattern recognition performance in multi-category SVM learning.
method Developed a new optimization algorithm based on Frank-Wolfe framework for MC-SVM variants.
result Closed-form solutions for direction finding and line search in the Frank-Wolfe framework for MC-SVM.
Worst-case risk measures refer to the calculation of the largest value for risk measures when only partial information of the underlying distribution is available. For the popular risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), it is now known that their worst-case counterparts can be ev…
Naz and Chaudhry [3] established multiple closed-form solutions for the basic Lucas-Uzawa model. According to Boucekkine and Ruiz-Tamarit [1] and Chilarescu [2] unique closed-form solutions exist for the basic Lucas-Uzawa model. We equate expressions for variables h(t) and u(t). We provide here condition for the unique…
Gradient-based training and pruning for radial basis function networks in materials physics.
problem Interpretable and robust machine learning for materials physics problems.
method Gradient-based training and pruning of radial basis function networks with closed-form optimization criteria.
result Pruned models provide compact and interpretable versions of larger models, offering insights into atom-level migration processes.
Optimal liquidation strategy reduces risk and improves performance.
problem Risk-averse trader liquidating assets in volatile markets.
method Conditional Value-at-Risk (CVaR) objective, dynamic trading strategies, closed-form solutions.
result Dynamic policies outperform static and VWAP policies by 15-25%.
We develop a family of techniques to align word embeddings which are derived from different source datasets or created using different mechanisms (e.g., GloVe or word2vec). Our methods are simple and have a closed form to optimally rotate, translate, and scale to minimize root mean squared errors or maximize the averag…
Closed-form polynomial approximations replace MLPs in transformers, enabling new interpretability methods.
problem Replacing MLPs with polynomial approximations for transformer models.
method Theoretical derivation of closed-form least-squares approximations of MLPs and GLUs using polynomial functions.
result Polynomial approximations explain over 95% of MLP and GLU outputs' variance, enabling interpretability.
Study of Gaussian distributions using entropic Gromov-Wasserstein and inner product Gromov-Wasserstein.
problem Optimal transportation between Gaussian distributions with different dimensions.
method Entropic Gromov-Wasserstein and inner product Gromov-Wasserstein, with closed-form expressions and von Neumann's trace inequality.
result Closed-form expressions for the entropic IGW and its unbalanced variant between Gaussian distributions.
New estimator handles covariate shift with closed-form solution and super-efficiency.
problem Handling covariate shift in missing data and causal inference problems.
method Minimum Wasserstein distance estimation framework.
result Closed-form expression and super-efficiency relative to semiparametric efficient estimator.
The paper analyzes insurance contracts under distributional uncertainty using Bregman-Wasserstein divergence.
problem Optimal insurance contracts under distributional ambiguity.
method Utilizes Bregman-Wasserstein ball to characterize ambiguity sets, employs robust optimization.
result Derives optimal indemnity functions in closed form and studies their properties.
This paper is concerned with an optimal stock selling rule under a Markov chain model. The objective is to find an optimal stopping time to sell the stock so as to maximize an expected return. Solutions to the associated variational inequalities are obtained. Closed-form solutions are given in terms of a set of thresho…
The paper refines and generalizes worst-case law invariant convex risk measures.
problem Developing robust convex risk measures under uncertainty sets.
method Generalizing closed forms for worst-case law invariant convex risk measures with uncertainty sets based on norms and moment constraints.
result Explicit closed forms for convex risk measures are developed and assessed through numerical simulations.
Optimal dividend strategy in dual risk model is well studied in the literatures. But to the best of our knowledge, all the previous works assumes deterministic interest rate. In this paper, we study the optimal dividends strategy in dual risk model, under a stochastic interest rate, assuming the discounting factor foll…
This paper proposes a method to approximate non-Gaussian likelihoods in Gaussian Processes.
problem Approximating non-Gaussian likelihoods in Gaussian Processes.
method Proposes a piece-wise constant approximation for the inverse-link function.
result Yields a closed form solution for the SVGP lower bound.
Study finds equivalence between MMV and MV preferences with conic constraints.
problem Monotone mean-variance portfolio selection under conic constraints.
method Closed-form solutions for optimal strategies under MMV and MV preferences.
result Optimal strategies coincide with and without the conic constraint.