Related papers: Robust No-Arbitrage under Projective Determinacy

Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from…

We consider a nondominated model of a discrete-time financial market where stocks are traded dynamically, and options are available for static hedging. In a general measure-theoretic setting, we show that absence of arbitrage in a…

We formulate conditions for the solvability of the problem of robust utility maximization from final wealth in continuous time financial markets, without assuming weak compactness of the densities of the uncertainty set, as customary in the…

We prove the superhedging duality for a discrete-time financial market with proportional transaction costs under model uncertainty. Frictions are modeled through solvency cones as in the original model of [Kabanov, Y., Hedging and…

When uncertainty is modelled by a set of non-dominated and non-compact probability measures, a notion of essential supremum for a family of real-valued functions is developed in terms of upper semi-analytic functions. We show how the…

This paper addresses the question of how an arbitrage-free semimartingale model is affected when stopped at a random horizon. We focus on No-Unbounded-Profit-with-Bounded-Risk (called NUPBR hereafter) concept, which is also known in the…

We propose a kernel-based nonparametric framework for mean-variance optimization that enables inference on economically motivated shape constraints in finance, including positivity, monotonicity, and convexity. Many central hypotheses in…

We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only…

We propose a continuous time model for financial markets with proportional transactions costs and a continuum of risky assets. This is motivated by bond markets in which the continuum of assets corresponds to the continuum of possible…

The fundamental tension between availability and consistency shapes the design of distributed storage systems. Classical results capture extreme points of this trade-off: the CAP theorem shows that strong models like linearizability…

Choosing a deep neural network architecture is a fundamental problem in applications that require balancing performance and parameter efficiency. Standard approaches rely on ad-hoc engineering or computationally expensive validation on a…

We study robust stochastic optimization problems in the quasi-sure setting in discrete-time. The strategies in the multi-period-case are restricted to those taking values in a discrete set. The optimization problems under consideration are…

A pointwise definable model is one in which every object is definable without parameters. In a model of set theory, this property strengthens V=HOD, but is not first-order expressible. Nevertheless, if ZFC is consistent, then there are…

In this paper, we study the pricing of contracts in fixed income markets under volatility uncertainty in the sense of Knightian uncertainty or model uncertainty. The starting point is an arbitrage-free bond market under volatility…

The two main approaches in credit risk are the structural approach pioneered in Merton (1974) and the reduced-form framework proposed in Jarrow & Turnbull (1995) and in Artzner & Delbaen (1995). The goal of this article is to provide a…

We establish deterministic necessary and sufficient conditions for the no-arbitrage notions "no increasing profit" (NIP), "no strong arbitrage" (NSA) and "no unbounded profit with bounded risk" (NUPBR) in one-dimensional general diffusion…

We establish deterministic necessary and sufficient conditions for the no-arbitrage notions NA ("no arbitrage"), NUPBR ("no unbounded profit with bounded risk") and NFLVR ("no free lunch with vanishing risk") in general diffusion market…

Stochastic dominance is a preference relation of uncertain prospect defined over a class of utility functions. While this utility class represents basic properties of risk aversion, it includes some extreme utility functions rarely…

We present an approach, based on deep neural networks, that allows identifying robust statistical arbitrage strategies in financial markets. Robust statistical arbitrage strategies refer to trading strategies that enable profitable trading…

We present an algorithm for robust model predictive control with consideration of uncertainty and safety constraints. Our framework considers a nonlinear dynamical system subject to disturbances from an unknown but bounded uncertainty set.…