arXiv research

A general duality proof for Wasserstein distributionally robust optimization.

We study the convex duality method for robust utility maximization in the presence of a random endowment. When the underlying price process is a locally bounded semimartingale, we show that the fundamental duality relation holds true for a wide class of utility functions on the whole real line and unbounded random endo…

Paper develops duality theory for robust utility maximization in continuous time.

Study investigates duality and dual optimizers for various transport problems.

Study optimizes option pricing with robust strategies, ensuring consistency with vanilla option prices.

A new robust Wasserstein distance is proposed to handle outliers in probability distributions.

We price and hedge American options robustly in continuous time.

We investigate pricing-hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, e.g. a family of European options, only statically. In the first part of the paper we consider an abstract setting, which includes the classical case with a fixed reference …

For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $λ\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading s…

New method reduces over-pessimism in Bayesian control under parameter uncertainty.

We consider the martingale optimal transport duality for càdlàg processes with given initial and terminal laws. Strong duality and existence of dual optimizers (robust semi-static superhedging strategies) are proved for a class of payoffs that includes American, Asian, Bermudan, and European options with intermediate m…

New method improves robustness of smoothed classifiers against adversarial attacks.

Develops a new duality between entropy martingale optimal transport and nonlinear pricing-hedging.

In this paper we derive robust super- and subhedging dualities for contingent claims that can depend on several underlying assets. In addition to strict super- and subhedging, we also consider relaxed versions which, instead of eliminating the shortfall risk completely, aim to reduce it to an acceptable level. This yie…

The paper shows how policy regularization acts like an adversary to improve robustness.

In this paper we define and develop the theory of the cohomology of a profinite group relative to a collection of closed subgroups. Having made the relevant definitions we establish a robust theory of cup products and use this theory to define profinite Poincaré duality pairs. We use the theory of groups acting on prof…

Duality for robust hedging with proportional transaction costs of path dependent European options is obtained in a discrete time financial market with one risky asset. Investor's portfolio consists of a dynamically traded stock and a static position in vanilla options which can be exercised at maturity. Both the stock …

Interest in generative models has grown tremendously in the past decade. However, their training performance can be adversely affected by contamination, where outliers are encoded in the representation of the model. This results in the generation of noisy data. In this paper, we introduce weighted conjugate feature dua…

Unified framework for DRO using OT with constraints.

Kernel DRO uses RKHS to optimize under distributional uncertainty.

We present a distributionally robust formulation of a stochastic optimization problem for non-i.i.d vector autoregressive data. We use the Wasserstein distance to define robustness in the space of distributions and we show, using duality theory, that the problem is equivalent to a finite convex-concave saddle point pro…

End-to-end portfolio system accounts for model risk.

We pursue robust approach to pricing and hedging in mathematical finance. We consider a continuous time setting in which some underlying assets and options, with continuous paths, are available for dynamic trading and a further set of European options, possibly with varying maturities, is available for static trading. …

Develops a method for solving optimal stopping problems with multiple exercise rights.

We establish a nondominated version of the optional decomposition theorem in a setting that includes jump processes with nonvanishing diffusion as well as general continuous processes. This result is used to derive a robust superhedging duality and the existence of an optimal superhedging strategy for general contingen…

DGKIP extends KIP for dataset distillation without bi-level optimization.

This work studies the strong duality of non-convex matrix factorization problems: we show that under certain dual conditions, these problems and its dual have the same optimum. This has been well understood for convex optimization, but little was known for non-convex problems. We propose a novel analytical framework an…

We create a robust hedging method for American options.

The martingale optimal transport aims to optimally transfer a probability measure to another along the class of martingales. This problem is mainly motivated by the robust superhedging of exotic derivatives in financial mathematics, which turns out to be the corresponding Kantorovich dual. In this paper we consider the…

Study robust utility maximization with uncertain continuous semimartingales.

We investigate asymmetry of information in the context of robust approach to pricing and hedging of financial derivatives. We consider two agents, one who only observes the stock prices and another with some additional information, and investigate when the pricing--hedging duality for the former extends to the latter. …

Operator-Valued Kernels (OVKs) and associated vector-valued Reproducing Kernel Hilbert Spaces provide an elegant way to extend scalar kernel methods when the output space is a Hilbert space. Although primarily used in finite dimension for problems like multi-task regression, the ability of this framework to deal with i…

Unified approach for robust and heavy-tailed mean estimation in high dimensions.

Tikhonov regularization is robust under specific martingale constraints in distributionally robust optimization.

This paper investigates calculations of robust XVA, in particular, credit valuation adjustment (CVA) and funding valuation adjustment (FVA) for over-the-counter derivatives under distributional uncertainty using Wasserstein distance as the ambiguity measure. Wrong way counterparty credit risk and funding risk can be ch…

Expands newsvendor model with moment constraints using Wasserstein distance.

Enhances survival analysis predictions with a robust learning approach.

We study a robust maximization problem from terminal wealth and consumption under a convex constraints on the portfolio. We state the existence and the uniqueness of the consumption-investment strategy by studying the associated quadratic backward stochastic differential equation (BSDE in short). We characterize the op…

Robust SVM optimization in Banach spaces tackles classification uncertainty.

New approach reduces simulator exploitation by improving strategic robustness.

New approach reduces simulator exploitation by learning robust models.

Let $X$ be a smooth compact manifold. We propose a geometric model for the group $K^0(X,\mathbb{R}/\mathbb{Z}).$ We study a well-defined and non-degenerate analytic duality pairing between $K^0(X,\mathbb{R}/\mathbb{Z})$ and its Pontryagin dual group, the Baum-Douglas geometric $K$-homology $K_0(X),$ whose pairing formu…

This work evaluates risks over time using robust measures and neural networks.

Develops robust learning framework under distributional perturbations.

This paper tackles robust control of noisy systems with uncertain distributions.

Since Hobson's seminal paper [D. Hobson: Robust hedging of the lookback option. In: Finance Stoch. (1998)] the connection between model-independent pricing and the Skorokhod embedding problem has been a driving force in robust finance. We establish a general pricing-hedging duality for financial derivatives which are s…

We consider a discrete time financial market with proportional transaction costs under model uncertainty, and study a numéraire-based semi-static utility maximization problem with an exponential utility preference. The randomization techniques recently developed in \cite{BDT17} allow us to transform the original proble…

Proves Poincaré duality for Hopf algebroids with bijective antipode.