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We study fully nonlinear second-order (forward) stochastic PDEs. They can also be viewed as forward path-dependent PDEs and will be treated as rough PDEs under a unified framework. For the most general fully n...
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 acce...
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 diffe...
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 expectation...
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 deri...
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...
An error occurred during the publication of an article in Probability, Uncertainty and Quantitative Risk. The article was published in volume 4 with a duplicate citation number.
The original article was published in Probability, Uncertainty and Quantitative Risk 2019 4:5
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The original article was published in Probability, Uncertainty and Quantitative Risk 2018 3:9
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 ...
The Publisher Correction to this article has been published in Probability, Uncertainty and Quantitative Risk 2019 4:7
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 r...
The paper is devoted to the Cauchy problem of backward stochastic super-parabolic equations with quadratic growth. We prove two Itô formulas in the whole space. Furthermore, we prove the existence of weak solu...
Conditional expectations (like, e.g., discounted prices in financial applications) are martingales under an appropriate filtration and probability measure. When the information flow arrives in a punctual way, ...
In this paper, we consider the mixed optimal control of a linear stochastic system with a quadratic cost functional, with two controllers—one can choose only deterministic time functions, called the determinis...
We show that the comparison results for a backward SDE with jumps established in Royer (Stoch. Process. Appl 116: 1358–1376, 2006) and Yin and Mao (J. Math. Anal. Appl 346: 345–358, 2008) hold under more simpl...
The Correction to this article has been published in Probability, Uncertainty and Quantitative Risk 2019 4:6
In this paper, we study strongly robust optimal control problems under volatility uncertainty. In the G-framework, we adapt the stochastic maximum principle to find necessary and sufficient conditions for the exi...
In this paper, we provide a valuation formula for different classes of actuarial and financial contracts which depend on a general loss process by using Malliavin calculus. Similar to the celebrated Black–Scho...
The main aim of this paper is to introduce the notion of risk excess measure, to analyze its properties, and to describe some basic construction methods. To compare the risk excess of one distribution Q w.r.t. a ...
Asset returns are modeled by locally bilateral gamma processes with zero covariations. Covariances are then observed to be consequences of randomness in variations. Support vector machine regressions on prices...
We study the existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations (BSVIEs) with jumps, where path-dependence means the dependence of the free term and genera...
We study an optimal investment problem under default risk where related information such as loss or recovery at default is considered as an exogenous random mark added at default time. Two types of agents who ...
The objective of this paper is to provide a comprehensive study of the no-arbitrage pricing of financial derivatives in the presence of funding costs, the counterparty credit risk and market frictions affectin...
We consider the class of affine LIBOR models with multiple curves, which is an analytically tractable class of discrete tenor models that easily accommodates positive or negative interest rates and positive sp...
We study robust notions of good-deal hedging and valuation under combined uncertainty about the drifts and volatilities of asset prices. Good-deal bounds are determined by a subset of risk-neutral pricing meas...
We develop a dynamic optimization framework to assess the impact of funding costs on credit swap investments. A defaultable investor can purchase CDS upfronts, borrow at a rate depending on her credit quality,...
One of the fundamental issues in Control Theory is to design feedback controls. It is well-known that, the purpose of introducing Riccati equations in the study of deterministic linear quadratic control proble...
This paper provides sufficient conditions for the time of bankruptcy (of a company or a state) for being a totally inaccessible stopping time and provides the explicit computation of its compensator in a frame...
The paper presents a comprehensive model of a banking system that integrates network effects, bankruptcy costs, fire sales, and cross-holdings. For the integrated financial market we prove the existence of a p...
Risks embedded in asset price dynamics are taken to be accumulations of surprise jumps. A Markov pure jump model is formulated on making variance gamma parameters deterministic functions of the price level. Es...
We apply to the concrete setup of a bank engaged into bilateral trade portfolios the XVA theoretical framework of (Albanese and Crépey2017), whereby so-called contra-liabilities and cost of capital are charged b...
In this introductory paper to the issue, I will travel through the history of how quantitative finance has developed and reached its current status, what problems it is called to address, and how they differ f...
We show the well-posedness of backward stochastic differential equations containing an additional drift driven by a path of finite q-variation with q∈[1,2). In contrast to previous work, we apply a direct fixpoin...
G-Brownian motion has a very rich and interesting new structure that nontrivially generalizes the classical Brownian motion. Its quadratic variation process is also a continuous process with independent and st...
In this work we give a comprehensive overview of the time consistency property of dynamic risk and performance measures, focusing on a the discrete time setup. The two key operational concepts used throughout ...
Default probability distributions are often defined in terms of their conditional default probability distribution, or their hazard rate. By their definition, they imply a unique probability density function. ...
In this paper, we study the recursive stochastic optimal control problems. The control domain does not need to be convex, and the generator of the backward stochastic differential equation can contain z. We obtai...
In this paper, a new numerical scheme for a class of coupled forward-backward stochastic differential equations (FBSDEs) is proposed by using branching particle systems in a random environment. First, by the f...
This paper studies the backward-forward linear-quadratic-Gaussian (LQG) games with major and minor agents (players). The state of major agent follows a linear backward stochastic differential equation (BSDE) and ...
We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weighting matrices in the cost functional are allo...
In this paper, we propose a new type of viscosity solutions for fully nonlinear path-dependent PDEs. By restricting the solution to a pseudo-Markovian structure defined below, we remove the uniform non-degener...
We consider the problem of approximation of the solution of the backward stochastic differential equations in Markovian case. We suppose that the forward equation depends on some unknown finite-dimensional par...
We consider a strictly pathwise setting for Delta hedging exotic options, based on Föllmer’s pathwise Itô calculus. Price trajectories are d-dimensional continuous functions whose pathwise quadratic variations an...
An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost functional. The coefficients and the weighting matrices in the cost functional are all assum...
Allowing for correlated squared returns across two consecutive periods, portfolio theory for two periods is developed. This correlation makes it necessary to work with non-Gaussian models. The two-period conic...
