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We study the problem of assessing the robustness of counterfactual explanations for deep learning models. We focus on $\textit{plausible model shifts}$ altering model parameters and propose a novel framework to reason about the robustness…

Nonparametric estimation of a mixing distribution based on data coming from a mixture model is a challenging problem. Beyond estimation, there is interest in uncertainty quantification, e.g., confidence intervals for features of the mixing…

In this paper we study dynamic pricing mechanism of contingent claims. A typical model of such pricing mechanism is the so-called g-expectation $E^g_{s,t}[X]$ defined by the solution of the backward stochastic differential equation with…

This paper aims to provide a simple modelling of speculative bubbles and derive some quantitative properties of its dynamical evolution. Starting from a description of individual speculative behaviours, we build and study a second order…

In this paper, we propose the uncertain volatility models with stochastic bounds. Like the regular uncertain volatility models, we know only that the true model lies in a family of progressively measurable and bounded processes, but instead…

This paper develops a model-free framework for static fixed-income pricing and the replication of liability cash flows. We show that the absence of static arbitrage across a universe of fixed-income instruments is equivalent to the…

We present here a regress later based Monte Carlo approach that uses neural networks for pricing high-dimensional contingent claims. The choice of specific architecture of the neural networks used in the proposed algorithm provides for…

In Part II of this paper, we concentrate our analysis on the price dynamical model with the moving average rules developed in Part I of this paper. By decomposing the excessive demand function, we reveal that it is the interplay between…

Counterfactual explanations are attracting significant attention due to the flourishing applications of machine learning models in consequential domains. A counterfactual plan consists of multiple possibilities to modify a given instance so…

We address the challenges of modeling high-frequency integer price changes in financial markets using continuous distributions, particularly the Student's t-distribution. We demonstrate that traditional GARCH models, which rely on…

This paper proposes a risk-averse approach to energy storage price arbitrage, leveraging conformal uncertainty quantification for electricity price predictions. The method addresses the significant challenges posed by the inherent…

We provide a model-free pricing-hedging duality in continuous time. For a frictionless market consisting of $d$ risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging…

In this paper, we investigate the precise local large deviation probabilities for random sums of independent real-valued random variables with a common distribution $F$, where $F(x+\Delta)=F((x, x+T])$ is an $\mathcal{O}$-regularly varying…

We derive a backward and forward nonlinear PDEs that govern the implied volatility of a contingent claim whenever the latter is well-defined. This would include at least any contingent claim written on a positive stock price whose payoff at…

We study utility indifference prices and optimal purchasing quantities for a non-traded contingent claim in an incomplete semi-martingale market with vanishing hedging errors. We make connections with the theory of large deviations. We…

We consider the robust pricing and hedging of American options in a continuous time setting. We assume asset prices are continuous semimartingales, but we allow for general model uncertainty specification via adapted closed convex…

We propose a method to assess the intrinsic risk carried by a financial position $X$ when the agent faces uncertainty about the pricing rule assigning its present value. Our approach is inspired by a new interpretation of the quasiconvex…

In this paper, we present a probabilistic adaptation of an Assume/Guarantee contract formalism. For the sake of generality, we assume that the extended state machines used in the contracts and implementations define sets of runs on a given…

We analyze the relative price change of assets starting from basic supply/demand considerations subject to arbitrary motivations. The resulting stochastic differential equation has coefficients that are functions of supply and demand. We…

Inspired by previous work on the constraints that duality imposes on beta functions of spin models, we propose a consistency condition between those functions and RG flows at different points in coupling constant space. We show that this…