Related papers: Robust No-Arbitrage under Projective Determinacy
This paper studies the dynamic programming principle for general convex stochastic optimization problems introduced by Rockafellar and Wets in [30]. We extend the applicability of the theory by relaxing compactness and boundedness…
In practical optimization problems, we typically model uncertainty as a random variable though its true probability distribution is unobservable to the decision maker. Historical data provides some information of this distribution that we…
Predictive algorithms inform consequential decisions in settings with selective labels: outcomes are observed only for units selected by past decision makers. This creates an identification problem under unobserved confounding -- when…
In this article, we show necessary and sufficient conditions for a function to transform a continuous Markov semimartingale to a semimartingale. As a result, the no-arbitrage principle guarantees the differentiability of asset prices with…
In this paper we demonstrate both theoretically as well as numerically that neural networks can detect model-free static arbitrage opportunities whenever the market admits some. Due to the use of neural networks, our method can be applied…
In a discrete time setting, we study the central problem of giving a fair price to some financial product. For several decades, the no-arbitrage conditions and the martingale measures have played a major role for solving this problem. We…
Uncertainty estimation in machine learning has traditionally focused on the prediction stage, aiming to quantify confidence in model outputs while treating learned representations as deterministic and reliable by default. In this work, we…
A standing assumption in the literature on proportional transaction costs is efficient friction. Together with robust no free lunch with vanishing risk, it rules out strategies of infinite variation, as they usually appear in frictionless…
The general method is proposed for constructing a family of martingale measures for a wide class of evolution of risky assets. The sufficient conditions are formulated for the evolution of risky assets under which the family of equivalent…
Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…
We consider a discrete time financial market with proportional transaction costs under model uncertainty, and study a num\'eraire-based semi-static utility maximization problem with an exponential utility preference. The randomization…
Decision maker's preferences are often captured by some choice functions which are used to rank prospects. In this paper, we consider ambiguity in choice functions over a multi-attribute prospect space. Our main result is a robust…
We consider the problem of computing the maximal invariant set of discrete-time black-box nonlinear systems without analytic dynamical models. Under the assumption that the system is asymptotically stable, the maximal invariant set…
Non-prehensile manipulation such as pushing is typically subject to uncertain, non-smooth dynamics. However, modeling the uncertainty of the dynamics typically results in intractable belief dynamics, making data-efficient planning under…
Experimental results on market behavior establish a lower stability and efficiency of markets for durable re-tradable assets compared to markets for non-durable, or perishable, goods. In this chapter, we revisit this known but…
This paper studies an equity market of stochastic dimension, where the number of assets fluctuates over time. In such a market, we develop the fundamental theorem of asset pricing, which provides the equivalence of the following statements:…
We study projective functions. We prove that projective functions generalise lower and upper-semianalytic ones while being stable by composition and difference. We show that the class of projective functions is closed under sums,…
The last decade witnessed an explosion in the availability of data for operations research applications. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization…
We use a decision-theoretic framework to study the problem of forecasting discrete outcomes when the forecaster is unable to discriminate among a set of plausible forecast distributions because of partial identification or concerns about…
A pricing principle is introduced for non-attainable $q$-exponential bounded contingent claims in an incomplete Brownian motion market setting. The buyer evaluates the contingent claim under the ``distorted Radon-Nikodym derivative'' and…