We consider portfolio optimization in futures markets. We model the entire futures price curve at once as a solution of a stochastic partial differential equation. The agents objective is to maximize her utility from the final wealth when investing in futures contracts. We study a class of futures price curve models wh…
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48 results for “finite-dimensional optimization problem”
We propose a method for pricing American options whose pay-off depends on the moving average of the underlying asset price. The method uses a finite dimensional approximation of the infinite-dimensional dynamics of the moving average process based on a truncated Laguerre series expansion. The resulting problem is a fin…
Survey of open problems in finite-dimensional integrable systems.
problem Open problems in finite-dimensional integrable systems.
method None specified; survey of existing open problems.
result Many open problems were identified from a conference.
Study bounds financial path expectations using martingale distributions.
problem Bounding path-dependent financial expectations over martingale distributions.
method Relaxed martingale optimal transport problem, approximated via linear programming.
result Empirical relaxation can be approximated within O(n^(-1/2)) error.
The paper extends lossy coding to nonlinear latent representations.
problem Learning finite-dimensional coding schemes with nonlinear reconstruction maps.
method Generalizes Maurer--Pontil framework to nonlinear maps, connects to generative modeling, and provides generalization bounds.
result Established a connection to approximate generative modeling and presented generalization bounds.
In this paper, we develop several related finite dimensional variational principles for discrete optimal transport (DOT), Minkowski type problems for convex polytopes and discrete Monge-Ampere equation (DMAE). A link between the discrete optimal transport, discrete Monge-Ampere equation and the power diagram in computa…
This paper solves nonparametric estimation of continuous DPPs using kernel methods.
problem Estimating continuous Determinantal Point Processes (DPPs) without assuming a parametric form.
method Developed a fixed point algorithm based on a representer theorem for nonnegative functions in RKHS.
result Demonstrated a finite-dimensional problem for nonparametric MLE of continuous DPPs.
The paper extends LDDMM framework to include Lie group actions in large deformation shape registration.
problem Modeling smooth, invertible transformations between shapes using Lie groups and diffeomorphisms.
method Develops a registration model that decouples the actions of Lie groups and diffeomorphisms, using semidirect products and right-invariant sub-Riemannian structures.
result Joint optimization over both deformation groups improves registration accuracy and disentangles contributions.
Survey of recent results on homogeneous finite-dimensional spaces.
problem Understanding properties of homogeneous finite-dimensional spaces.
method Discussion of recent results and unsolved problems.
result Discussion of recent results and unsolved problems.
We approximate the Sobolev discrepancy for finite dimensional kernels from samples.
problem Estimating the Sobolev discrepancy for complex models from finite data.
method Approximating the Sobolev discrepancy using finite samples and analyzing the approximation error.
result The Sobolev discrepancy can be approximated from finite samples and its error depends on the approximation and statistical errors.
The purpose of this paper is to show that in a finite dimensional metric space with Alexandrov's curvature bounded below, Monge's transport problem for the quadratic cost admits a unique solution.
This paper refines the Gaussian Sinkhorn algorithm for general multivariate models.
problem Finite-dimensional solutions for general Gaussian multivariate models.
method Recursive formulation of the Sinkhorn algorithm for Gaussian models, including closed form expressions of entropic transport maps and Schrödinger bridges.
result Refined convergence analysis of Gaussian Sinkhorn algorithms.
Minimal Gaussian surface area is achieved by cones over a regular simplex for sets partitioning .
problem Finding the minimal Gaussian surface area of sets partitioning .
method Volume-preserving variations of the sets, avoiding matrix-valued partial differential inequalities.
result Strengthened Milman-Neeman Gaussian multi bubble theorem and first known dimension-independent bounds for the Plurality is Stablest Conjecture.
Computation of optimal transport and related hedging problems via penalization and neural networksmath.OC
Paper uses neural networks to solve complex transport problems.
problem Optimal transport and related hedging problems.
method Penalization and neural networks to solve optimization problems.
result Effective solution to multi-marginal, martingale optimal transport problems.
A continuous selection for optimal portfolios under convex risk measures does not always existq-fin.MF
Continuous selections for optimal portfolios under convex risk measures fail in finite-dimensional settings.
problem Finding optimal financial positions with continuous selections under convex risk measures.
method Analyzing set-valued maps in finite-dimensional settings with convex risk measures.
result Continuous selections do not always exist for optimal portfolios under convex risk measures.
2-dimensional Kähler-Einstein metrics induced by finite dimensional complex projective spacesmath.DG
Solves classical problem with Kähler-Einstein metrics in complex projective spaces.
problem Classical problem of non-isometric bidimensional Kähler-Einstein submanifolds.
method Listed complete non-isometric bidimensional rotation invariant Kähler-Einstein submanifolds.
result Solves the classical problem in the specified case.
Separates estimation and control in risk-sensitive investment problems with partial observation.
problem Risk-sensitive investment problems with incomplete observation.
method Investigates separability of a general class of risk-sensitive investment management problems using a finite-dimensional filter.
result The separated problem is strictly equivalent to the original control problem.
Optimal risk sharing without convex preferences using aggregate convexity.
problem Risk sharing among non-convex preferences.
method Aggregate convexity principles and Lyapunov convexity, combined with approximation arguments for law invariant risk measures.
result Derivation of a computationally tractable formula for the conjugate of the value function.
A new method optimizes kernels for GANs and SVMs using mean-field theory.
problem Optimizing kernels for GANs and SVMs in a distributionally robust setting.
method Distributionally robust optimization, Monte-Carlo SAA, particle SGD, mean-field analysis.
result The method improves kernel learning for hypothesis testing and achieves better test power.
We study the optimal stopping problem of pricing an American Put option on a Zero Coupon Bond (ZCB) in the Musiela's parametrization of the Heath-Jarrow-Morton (HJM) model for forward interest rates. First we show regularity properties of the price function by probabilistic methods. Then we find an infinite dimensional…
The Lax-Hopf formula simplifies the value function of an intertemporal optimization (infinite dimensional) problem associated with a convex transaction-cost function which depends only on the transactions (velocities) of a commodity evolution: it states that the value function is equal to the marginal fonction of a fin…
This manuscript studies statistical properties of linear classifiers obtained through minimization of an unregularized convex risk over a finite sample. Although the results are explicitly finite-dimensional, inputs may be passed through feature maps; in this way, in addition to treating the consistency of logistic reg…
We show that a continuous local semiflow of -maps on a finite-dimensional -manifold M can be embedded into a local -flow on M under some weak (necessary) assumptions. This result is applied to an open problem in [fil/tei:01]. We prove that finite-dimensional realizations for interest rate models are high…
New bounds for adaptive control in high dimensions without fixed state space.
problem Adaptive control of linear systems in high or infinite dimensions.
method Novel perturbation bound for certainty equivalence, scaling with prediction error.
result First regret bounds for LQR in infinite dimensional systems, independent of ambient dimension.
The paper studies multi-curve interest rate models and their consistency and finite-dimensional realizations.
problem Consistency and existence of finite-dimensional realizations for multi-curve interest rate models.
method Geometric approach, characterizing consistency and existence of finite-dimensional realizations for multi-curve models.
result Characterization of consistency and existence of finite-dimensional realizations for multi-curve models.
Study optimizes growth rate for investors with long-only constraints.
problem Maximizing growth rate under drift uncertainty and long-only constraints.
method Developed a finite dimensional approximation for concave functionally generated portfolios.
result Proved uniqueness and existence for optimal portfolios under long-only constraints.
This paper tackles constrained statistical learning problems by proposing a new approach.
problem Statistical learning problems with constraints are challenging and scarce.
method Directly tackling the constrained problem using finite dimensional parameterizations, sample averages, and duality theory.
result We bound the empirical duality gap, showing the effectiveness of the constrained formulation.
New algorithm learns optimal resource allocation in wireless systems without models.
problem Learning optimal resource allocation in wireless systems without system models.
method Developed a model-free primal-dual algorithm using smoothed surrogates of constrained problems.
result The algorithm can make the gap between optimal values and dual values arbitrarily small.
Infinite-dimensional polynomial diffusions preserve tractability of finite-dimensional counterparts.
problem Modeling and analyzing infinite-dimensional probability measure-valued diffusions.
method Introduced polynomial diffusions, transferred properties from finite to infinite dimensions, and proved well-posedness of martingale problems.
result Tractability of finite-dimensional polynomial processes is preserved in the infinite-dimensional setting.
Optimal Bond Portfoliosmath.OC
We aim to construct a general framework for portfolio management in continuous time, encompassing both stocks and bonds. In these lecture notes we give an overview of the state of the art of optimal bond portfolios and we re-visit main results and mathematical constructions introduced in our previous publications (Ann.…
The purpose of this paper is to study finite dimensional equivariant moduli problems from the viewpoint of stratification theory. We show that there exists a stratified obstruction system for a finite dimensional equivariant moduli problem. In addition, we define a coindex for a G-vector bundle which is determined by t…
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth and invertible transformation that maps a simple distribution to the desired ma…
Linear regression can overfit without harm when data is high-dimensional.
problem Understanding when a perfect fit to noisy training data in linear regression leads to accurate predictions.
method Characterization of linear regression problems with a minimum norm interpolating prediction rule that has near-optimal prediction accuracy.
result Overparameterization is essential for benign overfitting in this setting, and the number of unimportant prediction directions must exceed the sample size.
Optimal maps and exponentiation on finite dimensional spaces with Ricci curvature bounded from belowmath.DG
We prove existence and uniqueness of optimal maps on spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result naturally leads to the notion of exponentiation.
Integrates side information for robust portfolio optimization.
problem Portfolio optimization under uncertainty and side information.
method Distributionally robust optimization with optimal transport ambiguity set.
result The problem can be reformulated as a finite-dimensional optimization problem.
Neural Jump ODEs extend to infinite-dimensional function spaces for optimal prediction.
problem Handling continuous-time stochastic processes in infinite-dimensional function spaces.
method Developing a new approximation strategy for infinite-dimensional function-valued processes.
result Proved convergence of the NJ-ODE to the optimal prediction process.
Optimizes risk-neutral probabilities for derivative pricing.
problem Deriving bounds on derivative values under multiple risk-neutral scenarios.
method Convex optimization over the set of risk-neutral probability distributions.
result Tractable finite-dimensional optimization problems for pricing.
The paper connects moment maps to the stability of holomorphic fibrations.
problem Stability of holomorphic fibrations.
method Use of moment maps and K-stability criteria.
result Existence of optimal symplectic connections implies stability of fibrations.
Researchers find a list of non-isometric toric para-Kaehler-Einstein manifolds.
problem Finding a complete list of mutually non-isometric Kaehler-Einstein manifolds immersed in a finite-dimensional Kaehler space form.
method Analytical approach to find mutually non-isometric toric para-Kaehler-Einstein manifolds.
result A list of mutually non-isometric toric para-Kaehler-Einstein manifolds analytically immersed in a finite-dimensional para-Kaehler space form.
Expands newsvendor model with moment constraints using Wasserstein distance.
problem Optimizing order quantity under distributional ambiguity.
method Formulates infinite dimensional primal problem, derives finite dimensional dual problem using problem of moments duality.
result Distributional ambiguity affects optimal order quantity and profits/costs.
This study analyzes the quadratic Wasserstein metric's effects on inverse data matching.
problem Analyzing the quadratic Wasserstein metric's impact on inverse data matching.
method Characterizes and numerically analyzes the smoothing effect and convexity improvement of distance.
result The distance improves convexity and reduces resolution for reconstructed objects at a given noise level.
-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler divergence, chi-squared divergence, squared Hellinger distance, total variation distance e…
Study improves learning algorithms for convex polyhedra in Hilbert spaces.
problem Learning convex polyhedra in Hilbert spaces.
method Proposes an algorithm for learning a polyhedron in a Hilbert space.
result Correctly classifies at least 1-ε of the distribution with high probability.
We propose a finite dimensional variational principle on triangulated 3-manifolds so that its critical points are related to solutions to Thurston's gluing equation and Haken's normal surface equation. The action functional is the volume. This is a generalization of an earlier program by Casson and Rivin for compact 3-…
We consider a class of operator-induced norms, acting as finite-dimensional surrogates to the L2 norm, and study their approximation properties over Hilbert subspaces of L2 . The class includes, as a special case, the usual empirical norm encountered, for example, in the context of nonparametric regression in reproduci…
We explore the robust replication of forward-start straddles given quoted (Call and Put options) market data. One approach to this problem classically follows semi-infinite linear programming arguments, and we propose a discretisation scheme to reduce its dimensionality and hence its complexity. Alternatively, one can …
Develops a finite construction for self-duality and related moduli spaces over Riemann surfaces.
problem Constructing moduli spaces over Riemann surfaces.
method Finite-dimensional construction using holomorphic symplectic reduction.
result Moduli spaces over Riemann surfaces as stratified holomorphic symplectic spaces.
Mean-variance dynamic portfolio allocation with transaction costs: a Wiener chaos expansion approachq-fin.PM
This paper proposes a new method to optimize portfolio allocation with transaction costs using Wiener chaos expansion.
problem Optimizing portfolio allocation with transaction costs in multi-period settings.
method Wiener chaos expansion approach to represent and solve the optimization problem.
result The proposed method finds an optimal strategy for portfolio allocation with transaction costs.