wanyu/IteraTeR_full_sent huggingface dataset:
Original:  In this setting, we present a thorough analysis of the relationship between order closedness of a convex set \mathcal{C ] in L^\Phi and the closedness of \mathcal{C topology \sigma(L^\Phi,L^\Psi) , culminating in the following surprising result:If (and only if) an Orlicz function \Phi and its conjugate \Psi both fail the \Delta_2-condition, then there exists a coherent risk measure on L^\Phi that has the Fatou property but does not admit a dual representation via L^{\Psi .
Revised:  In this setting, we present a thorough analysis of the relationship between order closedness of a convex set \mathcal{C ] in L^\Phi and the closedness of \mathcal{C topology \sigma(L^\Phi,L^\Psi) If (and only if) an Orlicz function \Phi and its conjugate \Psi both fail the \Delta_2-condition, then there exists a coherent risk measure on L^\Phi that has the Fatou property but does not admit a dual representation via L^{\Psi .
Edit intent: clarity
Original:  In this setting, we present a thorough analysis of the relationship between order closedness of a convex set \mathcal{C ] in L^\Phi and the closedness of \mathcal{C topology \sigma(L^\Phi,L^\Psi) , culminating in the following surprising result:If (and only if) an Orlicz function \Phi and its conjugate \Psi both fail the \Delta_2-condition, then there exists a coherent risk measure on L^\Phi that has the Fatou property but does not admit a dual representation via L^{\Psi .
Revised:  In this setting, we present a thorough analysis of the relationship between order closedness of a convex set \mathcal{C ] in L^\Phi and the closedness of \mathcal{C topology \sigma(L^\Phi,L^\Psi) , culminating in the following surprising result: .
Edit intent: meaning-changed
Original:  In this setting, we present a thorough analysis of the relationship between order closedness of a convex set \mathcal{C ] in L^\Phi and the closedness of \mathcal{C topology \sigma(L^\Phi,L^\Psi) , culminating in the following surprising result:If (and only if) an Orlicz function \Phi and its conjugate \Psi both fail the \Delta_2-condition, then there exists a coherent risk measure on L^\Phi that has the Fatou property but does not admit a dual representation via L^{\Psi . This result answers an open problem in the representation theory of risk measures. In the second part of our study,we explore the representation problem for the pair (H^\Phi,H^\Psi) . This part complements the study for the pair (H ^\Phi,L^\Psi) investigated in 8%DIFDELCMD < ] %%% and the study for the pair (L^{\Phi,H^{\Psi})investigated in }%DIFDELCMD < [%%% 19 . This paper contains new results and developments on the interplay between topology and order in Orlicz spaces that are of independent interest\emph{  .
Revised:  In this setting, we present a thorough analysis of the relationship between order closedness of a convex set \mathcal{C ] in L^\Phi and the closedness of \mathcal{C topology \sigma(L^\Phi,L^\Psi) , culminating in the following surprising result:If (and only if) an Orlicz function \Phi and its conjugate \Psi both fail the \Delta_2-condition, then there exists a coherent risk measure on L^\Phi that has the Fatou property but does not admit a dual representation via L^{\Psi ; that is, a convex set is \sigma(L^\Phi,L^\Psi)-closed if and only if it is closed with respect to the bounded-\sigma(L^\Phi,L^\Psi) topology. As a result, we show that order closedness and \sigma(L ^\Phi,L^\Psi) investigated in 8%DIFDELCMD < ] %%% and the study for the pair (L^{\Phi,H^{\Psi})investigated in }%DIFDELCMD < [%%% 19 . This paper contains new results and developments on the interplay between topology and order in Orlicz spaces that are of independent interest\emph{ .
Edit intent: meaning-changed
Original:  This part complements the study for the pair (H ^\Phi,L^\Psi) investigated in 8%DIFDELCMD < ] %%% and the study for the pair (L^{\Phi,H^{\Psi})investigated in }%DIFDELCMD < [%%% 19 . This paper contains new results and developments on the interplay between topology and order in Orlicz spaces that are of independent interest\emph{  .
Revised:  This part complements the study for the pair (H ^\Phi,L^\Psi) 8%DIFDELCMD < ] %%% and the study for the pair (L^{\Phi,H^{\Psi})investigated in }%DIFDELCMD < [%%% 19 . This paper contains new results and developments on the interplay between topology and order in Orlicz spaces that are of independent interest\emph{ .
Edit intent: clarity
Original:  This part complements the study for the pair (H ^\Phi,L^\Psi) investigated in 8%DIFDELCMD < ] %%% and the study for the pair (L^{\Phi,H^{\Psi})investigated in }%DIFDELCMD < [%%% 19 . This paper contains new results and developments on the interplay between topology and order in Orlicz spaces that are of independent interest\emph{  .
Revised:  This part complements the study for the pair (H ^\Phi,L^\Psi) investigated in %DIFDELCMD < ] %%% and the study for the pair (L^{\Phi,H^{\Psi})investigated in }%DIFDELCMD < [%%% 19 . This paper contains new results and developments on the interplay between topology and order in Orlicz spaces that are of independent interest\emph{ .
Edit intent: clarity
Original:  This part complements the study for the pair (H ^\Phi,L^\Psi) investigated in 8%DIFDELCMD < ] %%% and the study for the pair (L^{\Phi,H^{\Psi})investigated in }%DIFDELCMD < [%%% 19 . This paper contains new results and developments on the interplay between topology and order in Orlicz spaces that are of independent interest\emph{  .
Revised:  This part complements the study for the pair (H ^\Phi,L^\Psi) investigated in 8%DIFDELCMD < ] %%% ,H^{\Psi})investigated in }%DIFDELCMD < [%%% 19 . This paper contains new results and developments on the interplay between topology and order in Orlicz spaces that are of independent interest\emph{ .
Edit intent: coherence
Original:  This part complements the study for the pair (H ^\Phi,L^\Psi) investigated in 8%DIFDELCMD < ] %%% and the study for the pair (L^{\Phi,H^{\Psi})investigated in }%DIFDELCMD < [%%% 19 . This paper contains new results and developments on the interplay between topology and order in Orlicz spaces that are of independent interest\emph{  .
Revised:  This part complements the study for the pair (H ^\Phi,L^\Psi) investigated in 8%DIFDELCMD < ] %%% and the study for the pair (L^{\Phi,H^{\Psi})investigated in }%DIFDELCMD < [%%% . This paper contains new results and developments on the interplay between topology and order in Orlicz spaces that are of independent interest\emph{ .
Edit intent: meaning-changed
Original:  This part complements the study for the pair (H ^\Phi,L^\Psi) investigated in 8%DIFDELCMD < ] %%% and the study for the pair (L^{\Phi,H^{\Psi})investigated in }%DIFDELCMD < [%%% 19 . This paper contains new results and developments on the interplay between topology and order in Orlicz spaces that are of independent interest\emph{  .
Revised:  This part complements the study for the pair (H ^\Phi,L^\Psi) investigated in 8%DIFDELCMD < ] %%% and the study for the pair (L^{\Phi,H^{\Psi})investigated in }%DIFDELCMD < [%%% 19 -closedness of convex sets in L^\Phi are equivalent if and only if either \Phi or \Psi satisfies the \Delta_2-condition. Using this, we prove the surprising result that:\emph{ .
Edit intent: meaning-changed
Original:  This part complements the study for the pair (H ^\Phi,L^\Psi) investigated in 8%DIFDELCMD < ] %%% and the study for the pair (L^{\Phi,H^{\Psi})investigated in }%DIFDELCMD < [%%% 19 . This paper contains new results and developments on the interplay between topology and order in Orlicz spaces that are of independent interest\emph{  .
Revised:  This part complements the study for the pair (H ^\Phi,L^\Psi) investigated in 8%DIFDELCMD < ] %%% and the study for the pair (L^{\Phi,H^{\Psi})investigated in }%DIFDELCMD < [%%% 19 . This paper contains new results and developments on the interplay between topology and order in Orlicz spaces that are of independent interest\emph{If (and only if) \Phi and \Psi both fail the \Delta_2-condition, then there exists a coherent risk measure on L^\Phi that has the Fatou property but fails the Fenchel-Moreau dual representation with respect to the dual pair (L^\Phi, L^\Psi) .
Edit intent: meaning-changed
Original:  This part complements the study for the pair (H ^\Phi,L^\Psi) investigated in 8%DIFDELCMD < ] %%% and the study for the pair (L^{\Phi,H^{\Psi})investigated in }%DIFDELCMD < [%%% 19 . This paper contains new results and developments on the interplay between topology and order in Orlicz spaces that are of independent interest\emph{  .
Revised:  This part complements the study for the pair (H ^\Phi,L^\Psi) investigated in 8%DIFDELCMD < ] %%% and the study for the pair (L^{\Phi,H^{\Psi})investigated in }%DIFDELCMD < [%%% 19 . This paper contains new results and developments on the interplay between topology and order in Orlicz spaces that are of independent interest\emph{ . A similar analysis is carried out for the dual pair of Orlicz hearts (H^\Phi,H^\Psi) .
Edit intent: meaning-changed
Original:   The first result in this paper reveals that in reasonable continuous time financial market  the super--replication price is prohibitively costly and leads to trivial buy--and--hold strategies.
Revised:  This can be viewed as a stochastic impulse control problem with a terminal state constraint. The first result in this paper reveals that in reasonable continuous time financial market the super--replication price is prohibitively costly and leads to trivial buy--and--hold strategies.
Edit intent: meaning-changed
Original:  The results are obtained under the assumption that both the dimension p and the sample size n tend to infinity such that  n ^{-1p^{1-\gamma} } \to c\in(0,+\infty) and \gamma\in 0, 1) . Under weak conditions imposed on the the underlying data generating process, we find the asymptotic equivalents to the optimal shrinkage intensities , prove their asymptotic normality, and estimate them consistently.
Revised:  The results are obtained under the assumption that both the dimension p and the sample size n tend to infinity such that p/ n ^{-1p^{1-\gamma} } \to c\in(0,+\infty) and \gamma\in 0, 1) . Under weak conditions imposed on the the underlying data generating process, we find the asymptotic equivalents to the optimal shrinkage intensities , prove their asymptotic normality, and estimate them consistently.
Edit intent: meaning-changed
Original:  The results are obtained under the assumption that both the dimension p and the sample size n tend to infinity such that  n ^{-1p^{1-\gamma} } \to c\in(0,+\infty) and \gamma\in 0, 1) . Under weak conditions imposed on the the underlying data generating process, we find the asymptotic equivalents to the optimal shrinkage intensities , prove their asymptotic normality, and estimate them consistently.
Revised:  The results are obtained under the assumption that both the dimension p and the sample size n tend to infinity such that n p^{1-\gamma} } \to c\in(0,+\infty) and \gamma\in 0, 1) . Under weak conditions imposed on the the underlying data generating process, we find the asymptotic equivalents to the optimal shrinkage intensities , prove their asymptotic normality, and estimate them consistently.
Edit intent: clarity
Original:  The results are obtained under the assumption that both the dimension p and the sample size n tend to infinity such that  n ^{-1p^{1-\gamma} } \to c\in(0,+\infty) and \gamma\in 0, 1) . Under weak conditions imposed on the the underlying data generating process, we find the asymptotic equivalents to the optimal shrinkage intensities , prove their asymptotic normality, and estimate them consistently.
Revised:  The results are obtained under the assumption that both the dimension p and the sample size n tend to infinity such that n ^{-1p^{1-\gamma} } \to c\in(0,+\infty) 0, 1) . Under weak conditions imposed on the the underlying data generating process, we find the asymptotic equivalents to the optimal shrinkage intensities , prove their asymptotic normality, and estimate them consistently.
Edit intent: coherence
Original:  The results are obtained under the assumption that both the dimension p and the sample size n tend to infinity such that  n ^{-1p^{1-\gamma} } \to c\in(0,+\infty) and \gamma\in 0, 1) . Under weak conditions imposed on the the underlying data generating process, we find the asymptotic equivalents to the optimal shrinkage intensities , prove their asymptotic normality, and estimate them consistently.
Revised:  The results are obtained under the assumption that both the dimension p and the sample size n tend to infinity such that n ^{-1p^{1-\gamma} } \to c\in(0,+\infty) and \gamma\in . Under weak conditions imposed on the the underlying data generating process, we find the asymptotic equivalents to the optimal shrinkage intensities , prove their asymptotic normality, and estimate them consistently.
Edit intent: coherence
Original:  The results are obtained under the assumption that both the dimension p and the sample size n tend to infinity such that  n ^{-1p^{1-\gamma} } \to c\in(0,+\infty) and \gamma\in 0, 1) . Under weak conditions imposed on the the underlying data generating process, we find the asymptotic equivalents to the optimal shrinkage intensities , prove their asymptotic normality, and estimate them consistently.
Revised:  The results are obtained under the assumption that both the dimension p and the sample size n tend to infinity such that n ^{-1p^{1-\gamma} } \to c\in(0,+\infty) and \gamma\in 0, 1) . Under weak conditions imposed on the underlying data generating process, we find the asymptotic equivalents to the optimal shrinkage intensities , prove their asymptotic normality, and estimate them consistently.
Edit intent: fluency
Original:  The results are obtained under the assumption that both the dimension p and the sample size n tend to infinity such that  n ^{-1p^{1-\gamma} } \to c\in(0,+\infty) and \gamma\in 0, 1) . Under weak conditions imposed on the the underlying data generating process, we find the asymptotic equivalents to the optimal shrinkage intensities , prove their asymptotic normality, and estimate them consistently.
Revised:  The results are obtained under the assumption that both the dimension p and the sample size n tend to infinity such that n ^{-1p^{1-\gamma} } \to c\in(0,+\infty) and \gamma\in 0, 1) . Under weak conditions imposed on the the underlying data generating process, we find the asymptotic equivalents to the optimal shrinkage intensities and estimate them consistently.
Edit intent: meaning-changed
Original:  At the end, an exhaustive simulation study and an application to real data are provided where the proposed estimator is compared with known benchmarks from the literature  .
Revised:  At the end, an exhaustive simulation study and an application to real data are provided where the proposed estimator is compared with known benchmarks from the literature . It turns out that the existent estimators of the mean vector including the suggested one converge to the sample mean vector when the true mean vector possesses unbounded Euclidean norm .
Edit intent: meaning-changed
Original:  The obtained non-parametric estimator for the high-dimensional mean vector has a simple structure and is proven to minimize asymptotically  with probability 1  the quadratic loss in the case of c\in(0,1).
Revised:  The proposed nonparametric estimator for the high-dimensional mean vector has a simple structure and is proven to minimize asymptotically with probability 1 the quadratic loss in the case of c\in(0,1).
Edit intent: clarity
Original:  The obtained non-parametric estimator for the high-dimensional mean vector has a simple structure and is proven to minimize asymptotically  with probability 1  the quadratic loss in the case of c\in(0,1).
Revised:  The obtained non-parametric estimator for the high-dimensional mean vector has a simple structure and is proven to minimize asymptotically , with probability 1 the quadratic loss in the case of c\in(0,1).
Edit intent: fluency
Original:  The obtained non-parametric estimator for the high-dimensional mean vector has a simple structure and is proven to minimize asymptotically  with probability 1  the quadratic loss in the case of c\in(0,1).
Revised:  The obtained non-parametric estimator for the high-dimensional mean vector has a simple structure and is proven to minimize asymptotically with probability 1 , the quadratic loss in the case of c\in(0,1).
Edit intent: fluency
Original:  The obtained non-parametric estimator for the high-dimensional mean vector has a simple structure and is proven to minimize asymptotically  with probability 1  the quadratic loss in the case of c\in(0,1).
Revised:  The obtained non-parametric estimator for the high-dimensional mean vector has a simple structure and is proven to minimize asymptotically with probability 1 the quadratic loss when c\in(0,1).
Edit intent: clarity
Original:  Our model resembles the strong degree of heterogeneity observed in empirical data and the parameters of the model can easily be fitted to market data . We derive asymptotic results that, based on these parameters, allow to determine the impact of local shocks  to the entire system and the wider economy.
Revised:  Our model resembles the strong degree of heterogeneity observed in empirical data and the parameters of the model can easily be fitted to real data sets. One of our main results allows us to determine the impact of local shocks to the entire system and the wider economy.
Edit intent: clarity
Original:  For networks with degree sequences without second moment,  a small number of initially defaulted banks can trigger a substantial default cascade even under the absence of so called contagious links. Paralleling regulatory discussions we determine minimal capital requirements for financial institutions sufficient to make the network resilient to small shocks  .
Revised:  For networks with degree sequences without second moment, a small number of initially defaulted banks can trigger a substantial default cascade . Our results complement and extend significantly earlier findings derived in the configuration model where the existence of a second moment of the degree distribution is assumed. Moreover, paralleling regulatory discussions, we determine minimal capital requirements for financial institutions sufficient to make the network resilient to small shocks .
Edit intent: meaning-changed
Original:  Paralleling regulatory discussions we determine minimal capital requirements for financial institutions sufficient to make the network resilient to small shocks  .
Revised:  Paralleling regulatory discussions we determine minimal capital requirements for financial institutions sufficient to make the network resilient to small shocks . An appealing feature of these capital requirements is that they can be determined locally by each institution without knowing the complete network structure as they basically only depend on the institution's exposures to its counterparties .
Edit intent: meaning-changed
Original:  Our modeling framework consists of the equity which follows the dynamics of the Heston stochastic volatility model  and the stochastic interest rate  driven by the Cox-Ingersoll-Ross (CIR) process with full correlation structure  among the state variables.
Revised:  Our modeling framework consists of the equity which follows the dynamics of the Heston stochastic volatility model , and the stochastic interest rate driven by the Cox-Ingersoll-Ross (CIR) process with full correlation structure among the state variables.
Edit intent: fluency
Original:  Our modeling framework consists of the equity which follows the dynamics of the Heston stochastic volatility model  and the stochastic interest rate  driven by the Cox-Ingersoll-Ross (CIR) process with full correlation structure  among the state variables.
Revised:  Our modeling framework consists of the equity which follows the dynamics of the Heston stochastic volatility model and the stochastic interest rate is driven by the Cox-Ingersoll-Ross (CIR) process with full correlation structure among the state variables.
Edit intent: clarity
Original:  Our modeling framework consists of the equity which follows the dynamics of the Heston stochastic volatility model  and the stochastic interest rate  driven by the Cox-Ingersoll-Ross (CIR) process with full correlation structure  among the state variables.
Revised:  Our modeling framework consists of the equity which follows the dynamics of the Heston stochastic volatility model and the stochastic interest rate driven by the Cox-Ingersoll-Ross (CIR) process with full correlation structure imposed among the state variables.
Edit intent: clarity
Original:  Since one limitation of hybrid models is the unavailability of analytical pricing formula  of variance swaps  due to the non-affinity property , we obtain an efficient semi-closed form pricing formula of variance swaps for an approximation of the hybrid model via the derivation of characteristic functions.
Revised:  This full correlation structure possess the limitation to have fully analytical pricing formula of variance swaps due to the non-affinity property , we obtain an efficient semi-closed form pricing formula of variance swaps for an approximation of the hybrid model via the derivation of characteristic functions.
Edit intent: meaning-changed
Original:  Since one limitation of hybrid models is the unavailability of analytical pricing formula  of variance swaps  due to the non-affinity property , we obtain an efficient semi-closed form pricing formula of variance swaps for an approximation of the hybrid model via the derivation of characteristic functions.
Revised:  Since one limitation of hybrid models is the unavailability of analytical pricing formula for hybrid models of variance swaps due to the non-affinity property , we obtain an efficient semi-closed form pricing formula of variance swaps for an approximation of the hybrid model via the derivation of characteristic functions.
Edit intent: meaning-changed
Original:  Since one limitation of hybrid models is the unavailability of analytical pricing formula  of variance swaps  due to the non-affinity property , we obtain an efficient semi-closed form pricing formula of variance swaps for an approximation of the hybrid model via the derivation of characteristic functions.
Revised:  Since one limitation of hybrid models is the unavailability of analytical pricing formula of variance swaps , due to the non-affinity property , we obtain an efficient semi-closed form pricing formula of variance swaps for an approximation of the hybrid model via the derivation of characteristic functions.
Edit intent: fluency
Original:  Since one limitation of hybrid models is the unavailability of analytical pricing formula  of variance swaps  due to the non-affinity property , we obtain an efficient semi-closed form pricing formula of variance swaps for an approximation of the hybrid model via the derivation of characteristic functions.
Revised:  Since one limitation of hybrid models is the unavailability of analytical pricing formula of variance swaps due to the non-affinity property embedded in the model itself. We address this issue by obtaining an efficient semi-closed form pricing formula of variance swaps for an approximation of the hybrid model via the derivation of characteristic functions.
Edit intent: meaning-changed
Original: We derive bounds on the distribution function, therefore also on the Value-at-Risk, of \varphi(\mathbf X) where \varphi is an aggregation function and \mathbf X = (X_1, ... \dots ,X_d) is a random vector with known marginal distributions and partially known dependence structure.
Revised: We derive bounds on the distribution function, therefore also on the Value-at-Risk, of \varphi(\mathbf X) where \varphi is an aggregation function and \mathbf X = (X_1, \dots ,X_d) is a random vector with known marginal distributions and partially known dependence structure.
Edit intent: fluency