Marushkevych, Dmytro Popier, Alexandre
Published in
Probability, Uncertainty and Quantitative Risk

We use the functional Itô calculus to prove that the solution of a BSDE with singular terminal condition verifies at the terminal time: liminft→TY(t)=ξ=Y(T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\odds...

Tangpi, Ludovic
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Probability, Uncertainty and Quantitative Risk

It is well known that the minimal superhedging price of a contingent claim is too high for practical use. In a continuous-time model uncertainty framework, we consider a relaxed hedging criterion based on acceptable shortfall risks. Combining existing aggregation and convex dual representation theorems, we derive duality results for the minimal pri...

Han, Jiequn Long, Jihao
Published in
Probability, Uncertainty and Quantitative Risk

The recently proposed numerical algorithm, deep BSDE method, has shown remarkable performance in solving high-dimensional forward-backward stochastic differential equations (FBSDEs) and parabolic partial differential equations (PDEs). This article lays a theoretical foundation for the deep BSDE method in the general case of coupled FBSDEs. In parti...

Cohen, Samuel N.
Published in
Probability, Uncertainty and Quantitative Risk

We consider the problem of filtering an unseen Markov chain from noisy observations, in the presence of uncertainty regarding the parameters of the processes involved. Using the theory of nonlinear expectations, we describe the uncertainty in terms of a penalty function, which can be propagated forward in time in the place of the filter. We also in...

Ansari, Jonathan Rüschendorf, Ludger
Published in
Probability, Uncertainty and Quantitative Risk

For the class of (partially specified) internal risk factor models we establish strongly simplified supermodular ordering results in comparison to the case of general risk factor models. This allows us to derive meaningful and improved risk bounds for the joint portfolio in risk factor models with dependence information given by constrained specifi...

Singh, Saroja Kumar
Published in
Probability, Uncertainty and Quantitative Risk

Consider a single server queueing model which is observed over a continuous time interval (0,T], where T is determined by a suitable stopping rule. Let θ be the unknown parameter for the arrival process and θ̂T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usep...

Xu, Qing Xuan, Xiaohua (Michael)
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Probability, Uncertainty and Quantitative Risk

In this paper, we consider a class of nonlinear regression problems without the assumption of being independent and identically distributed. We propose a correspondent mini-max problem for nonlinear regression and give a numerical algorithm. Such an algorithm can be applied in regression and machine learning problems, and yields better results than...

Geiss, Christel Steinicke, Alexander
Published in
Probability, Uncertainty and Quantitative Risk

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Fadina, Tolulope Neufeld, Ariel Schmidt, Thorsten
Published in
Probability, Uncertainty and Quantitative Risk

We develop a one-dimensional notion of affine processes under parameter uncertainty, which we call nonlinear affine processes. This is done as follows: given a set Θ of parameters for the process, we construct a corresponding nonlinear expectation on the path space of continuous processes. By a general dynamic programming principle, we link this no...

Peng, Shige
Published in
Probability, Uncertainty and Quantitative Risk

The main achievement of this paper is the finding and proof of Central Limit Theorem (CLT, see Theorem 12) under the framework of sublinear expectation. Roughly speaking under some reasonable assumption, the random sequence {1/n(X1+⋯+Xn)}i=1∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{am...