wanyu/IteraTeR_full_sent huggingface dataset:
Original:  We establish existence and uniqueness of the optimal solution using convex duality on the product space \mathbb{L_{+}^{0}(\Omega\times[0,T],O,}%DIFDELCMD < \mathbb{P}%%% ) by defining the primal value function as depending on both the initial wealth and  initial standard of living.
Revised:  We establish existence and uniqueness of the optimal solution using convex duality on the product space \mathbb{L_{+}^{0}(\Omega\times[0,T],O,}%DIFDELCMD < \mathbb{P}%%% ) by defining the primal value function as depending on both the initial wealth and the initial standard of living.
Edit intent: fluency
Original:  We also provide market independent sufficient conditions on both stochastic discounting processes of the habit formation process and on the utility function for our original problem to be well posed and to modify the convex duality approach when the auxiliary dual process is not necessarily integrable.
Revised:  We also provide market independent sufficient conditions both on the stochastic discounting processes of the habit formation process and on the utility function for our original problem to be well posed and to modify the convex duality approach when the auxiliary dual process is not necessarily integrable.
Edit intent: fluency
Original:  We also provide market independent sufficient conditions on both stochastic discounting processes of the habit formation process and on the utility function for our original problem to be well posed and to modify the convex duality approach when the auxiliary dual process is not necessarily integrable.
Revised:  We also provide market independent sufficient conditions on both stochastic discounting processes and on the utility function for our original problem to be well posed and to modify the convex duality approach when the auxiliary dual process is not necessarily integrable.
Edit intent: clarity
Original:  We also provide market independent sufficient conditions on both stochastic discounting processes of the habit formation process and on the utility function for our original problem to be well posed and to modify the convex duality approach when the auxiliary dual process is not necessarily integrable.
Revised:  We also provide market independent sufficient conditions on both stochastic discounting processes of the habit formation process and on the utility function for the well-posedness of our original optimization problem. Under the same assumptions, we can carefully modify the classical proofs in the approach of convex duality analysis when the auxiliary dual process is not necessarily integrable.
Edit intent: meaning-changed
Original:  Introducing the set of auxiliary state processes and the modified dual space, we embed our original problem into an abstract time-separable utility maximization problem with a shadow random endowment on the product space . We establish existence_{+}^{0}(\Omega\times[0,T],O,}\mathbb{P} and uniqueness of the optimal solution  using convex duality by defining the primal value function as depending on two variables, i.e., the initial wealth and the initial standard of living.
Revised:  Introducing the set of auxiliary state processes and the modified dual space, we embed our original problem into an abstract time-separable utility maximization problem with a shadow random endowment on the product space \mathbb{L_{+}^{0}(\Omega\times[0,T],O,}\mathbb{P} and uniqueness of the optimal solution using convex duality by defining the primal value function as depending on two variables, i.e., the initial wealth and the initial standard of living.
Edit intent: coherence
Original:  We establish existence_{+}^{0}(\Omega\times[0,T],O,}\mathbb{P} and uniqueness of the optimal solution  using convex duality by defining the primal value function as depending on two variables, i.e., the initial wealth and the initial standard of living.
Revised:  We establish existence_{+}^{0}(\Omega\times[0,T],O,}\mathbb{P}). Existence and uniqueness of the optimal solution using convex duality by defining the primal value function as depending on two variables, i.e., the initial wealth and the initial standard of living.
Edit intent: coherence
Original:  We establish existence_{+}^{0}(\Omega\times[0,T],O,}\mathbb{P} and uniqueness of the optimal solution  using convex duality by defining the primal value function as depending on two variables, i.e., the initial wealth and the initial standard of living.
Revised:  We establish existence_{+}^{0}(\Omega\times[0,T],O,}\mathbb{P} and uniqueness of the optimal solution are established using convex duality by defining the primal value function as depending on two variables, i.e., the initial wealth and the initial standard of living.
Edit intent: coherence
Original:  We establish existence_{+}^{0}(\Omega\times[0,T],O,}\mathbb{P} and uniqueness of the optimal solution  using convex duality by defining the primal value function as depending on two variables, i.e., the initial wealth and the initial standard of living.
Revised:  We establish existence_{+}^{0}(\Omega\times[0,T],O,}\mathbb{P} and uniqueness of the optimal solution using convex duality approach, where the primal value function as depending on two variables, i.e., the initial wealth and the initial standard of living.
Edit intent: clarity
Original:  We establish existence_{+}^{0}(\Omega\times[0,T],O,}\mathbb{P} and uniqueness of the optimal solution  using convex duality by defining the primal value function as depending on two variables, i.e., the initial wealth and the initial standard of living.
Revised:  We establish existence_{+}^{0}(\Omega\times[0,T],O,}\mathbb{P} and uniqueness of the optimal solution using convex duality by defining the primal value function is defined on two variables, i.e., the initial wealth and the initial standard of living.
Edit intent: clarity
Original:  Introducing the set of auxiliary state processes and the modified dual space, we embed our original problem into a time-separable utility maximization problem with a shadow random endowment on the product space L _{+^{0}(\Omega\times[0,T],O,}%DIFDELCMD < \mathbb{P}%%%  ],}\mathbb{P} ).
Revised:  Introducing the set of auxiliary state processes and the modified dual space, we embed our original problem into a time-separable utility maximization problem with a shadow random endowment on the product space L ^{0}(\Omega\times[0,T],O,}%DIFDELCMD < \mathbb{P}%%% ],}\mathbb{P} ).
Edit intent: meaning-changed
Original:  Introducing the set of auxiliary state processes and the modified dual space, we embed our original problem into a time-separable utility maximization problem with a shadow random endowment on the product space L _{+^{0}(\Omega\times[0,T],O,}%DIFDELCMD < \mathbb{P}%%%  ],}\mathbb{P} ).
Revised:  Introducing the set of auxiliary state processes and the modified dual space, we embed our original problem into a time-separable utility maximization problem with a shadow random endowment on the product space L _{+^{0}(\Omega\times[0,T],O,}%DIFDELCMD < \mathbb{P}%%% _+^0(\Omega\times ],}\mathbb{P} ).
Edit intent: meaning-changed
Original:  Introducing the set of auxiliary state processes and the modified dual space, we embed our original problem into a time-separable utility maximization problem with a shadow random endowment on the product space L _{+^{0}(\Omega\times[0,T],O,}%DIFDELCMD < \mathbb{P}%%%  ],}\mathbb{P} ).
Revised:  Introducing the set of auxiliary state processes and the modified dual space, we embed our original problem into a time-separable utility maximization problem with a shadow random endowment on the product space L _{+^{0}(\Omega\times[0,T],O,}%DIFDELCMD < \mathbb{P}%%% 0,T],}\mathbb{P} ).
Edit intent: meaning-changed
Original:  Introducing the set of auxiliary state processes and the modified dual space, we embed our original problem into a time-separable utility maximization problem with a shadow random endowment on the product space L _{+^{0}(\Omega\times[0,T],O,}%DIFDELCMD < \mathbb{P}%%%  ],}\mathbb{P} ).
Revised:  Introducing the set of auxiliary state processes and the modified dual space, we embed our original problem into a time-separable utility maximization problem with a shadow random endowment on the product space L _{+^{0}(\Omega\times[0,T],O,}%DIFDELCMD < \mathbb{P}%%% ],\mathcal{O,}\mathbb{P} ).
Edit intent: meaning-changed
Original:  Existence and uniqueness of the optimal solution are established using convex duality approach, where the primal value function is defined on two variables, i.e. , the initial wealth and the initial standard of living.
Revised:  Existence and uniqueness of the optimal solution are established using convex duality approach, where the primal value function is defined on two variables, that is , the initial wealth and the initial standard of living.
Edit intent: coherence
Original:  These distributions are shown to be well described in the continuous approximation, which is then used to discuss the qualitative features of the protein equilibrium distributions as a function of the biological parameters in the fast mRNA regime  .
Revised:  These distributions are shown to be well described in the continuous approximation, which is used to discuss the qualitative features of the protein equilibrium distributions as a function of the biological parameters in the fast mRNA regime .
Edit intent: coherence
Original:  These distributions are shown to be well described in the continuous approximation, which is then used to discuss the qualitative features of the protein equilibrium distributions as a function of the biological parameters in the fast mRNA regime  .
Revised:  These distributions are shown to be well described in the continuous approximation, which is then used to discuss the qualitative features of the protein equilibrium distributions as a function of the biological parameters in the fast mRNA regime . The performance of the timescale approximation is assessed by comparison with simulations of the full stochastic system, and a good quantitative agreement is found for a wide range of parameter values. We show that either unimodal or bimodal equilibrium protein distributions can arise, and we discuss the auto-regulation mechanisms associated with bimodality .
Edit intent: meaning-changed
Original: We consider the problem of maximizing expected power util- ity from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the paper Shreve and Soner  (1994) . Similarly  to Kallsen and Muhle-Karbe  (2010)  , we derive a shadow price, that is, a frictionless price process with values in the bid-ask spread which leads to the same optimal policy .
Revised: We consider the problem of maximizing expected power utility from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the paper Shreve and Soner (1994) . Similarly to Kallsen and Muhle-Karbe (2010) , we derive a shadow price, that is, a frictionless price process with values in the bid-ask spread which leads to the same optimal policy .
Edit intent: fluency
Original: We consider the problem of maximizing expected power util- ity from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the paper Shreve and Soner  (1994) . Similarly  to Kallsen and Muhle-Karbe  (2010)  , we derive a shadow price, that is, a frictionless price process with values in the bid-ask spread which leads to the same optimal policy .
Revised: We consider the problem of maximizing expected power util- ity from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in Shreve and Soner (1994) . Similarly to Kallsen and Muhle-Karbe (2010) , we derive a shadow price, that is, a frictionless price process with values in the bid-ask spread which leads to the same optimal policy .
Edit intent: coherence
Original: We consider the problem of maximizing expected power util- ity from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the paper Shreve and Soner  (1994) . Similarly  to Kallsen and Muhle-Karbe  (2010)  , we derive a shadow price, that is, a frictionless price process with values in the bid-ask spread which leads to the same optimal policy .
Revised: We consider the problem of maximizing expected power util- ity from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the paper Shreve and Soner Ann. Appl. Probab. 4 (1994) . Similarly to Kallsen and Muhle-Karbe (2010) , we derive a shadow price, that is, a frictionless price process with values in the bid-ask spread which leads to the same optimal policy .
Edit intent: meaning-changed
Original: We consider the problem of maximizing expected power util- ity from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the paper Shreve and Soner  (1994) . Similarly  to Kallsen and Muhle-Karbe  (2010)  , we derive a shadow price, that is, a frictionless price process with values in the bid-ask spread which leads to the same optimal policy .
Revised: We consider the problem of maximizing expected power util- ity from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the paper Shreve and Soner (1994) 609-692 to Kallsen and Muhle-Karbe (2010) , we derive a shadow price, that is, a frictionless price process with values in the bid-ask spread which leads to the same optimal policy .
Edit intent: meaning-changed
Original: We consider the problem of maximizing expected power util- ity from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the paper Shreve and Soner  (1994) . Similarly  to Kallsen and Muhle-Karbe  (2010)  , we derive a shadow price, that is, a frictionless price process with values in the bid-ask spread which leads to the same optimal policy .
Revised: We consider the problem of maximizing expected power util- ity from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the paper Shreve and Soner (1994) . Similarly . Similar to Kallsen and Muhle-Karbe (2010) , we derive a shadow price, that is, a frictionless price process with values in the bid-ask spread which leads to the same optimal policy .
Edit intent: fluency
Original: We consider the problem of maximizing expected power util- ity from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the paper Shreve and Soner  (1994) . Similarly  to Kallsen and Muhle-Karbe  (2010)  , we derive a shadow price, that is, a frictionless price process with values in the bid-ask spread which leads to the same optimal policy .
Revised: We consider the problem of maximizing expected power util- ity from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the paper Shreve and Soner (1994) . Similarly to Kallsen and Muhle-Karbe Ann. Appl. Probab. 20 (2010) , we derive a shadow price, that is, a frictionless price process with values in the bid-ask spread which leads to the same optimal policy .
Edit intent: meaning-changed
Original: We consider the problem of maximizing expected power util- ity from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the paper Shreve and Soner  (1994) . Similarly  to Kallsen and Muhle-Karbe  (2010)  , we derive a shadow price, that is, a frictionless price process with values in the bid-ask spread which leads to the same optimal policy .
Revised: We consider the problem of maximizing expected power util- ity from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the paper Shreve and Soner (1994) . Similarly to Kallsen and Muhle-Karbe (2010) 1341-1358 , we derive a shadow price, that is, a frictionless price process with values in the bid-ask spread which leads to the same optimal policy .
Edit intent: meaning-changed
Original: We consider the problem of maximizing expected power util- ity from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the paper Shreve and Soner  (1994) . Similarly  to Kallsen and Muhle-Karbe  (2010)  , we derive a shadow price, that is, a frictionless price process with values in the bid-ask spread which leads to the same optimal policy . In doing so we explore and exploit the strong relationship between the shadow price and the Hamilton-Jacobi-Bellman-equation .
Revised: We consider the problem of maximizing expected power util- ity from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the paper Shreve and Soner (1994) . Similarly to Kallsen and Muhle-Karbe (2010) , we derive a shadow price, that is, a frictionless price process with values in the bid-ask spread which leads to the same optimal policy .
Edit intent: meaning-changed
Original:  To provide a better understanding of the kinetics of RNA secondary structure formation, we are interested in determining the asymptotic number of secondary structures that are %DIFDELCMD < {\em %%% locally optimal , with respect to a particular energy model.
Revised:  Motivated by the kinetics of RNA secondary structure formation, we are interested in determining the asymptotic number of secondary structures that are %DIFDELCMD < {\em %%% locally optimal , with respect to a particular energy model.
Edit intent: clarity
Original:  To provide a better understanding of the kinetics of RNA secondary structure formation, we are interested in determining the asymptotic number of secondary structures that are %DIFDELCMD < {\em %%% locally optimal , with respect to a particular energy model.
Revised:  To provide a better understanding of the kinetics of RNA secondary structure formation, we are interested in determining the asymptotic number of secondary structures that are %DIFDELCMD < {\em %%% locally optimal , with respect to a particular energy model.
Edit intent: fluency
Original:  In the Nussinov energy model, where each base pair contributes -1 towards the energy of the structure, locally optimal structures are exactly the %DIFDELCMD < {\em %%% saturated structures, for which we have previously shown that asymptotically, there are 1.07427\cdot n^{-3/2} \cdot 2.35467^n many saturated structures for a sequence of length n.
Revised:  In the Nussinov energy model, where each base pair contributes -1 towards the energy of the structure, locally optimal structures are exactly the %DIFDELCMD < {\em %%% saturated structures, for which we have previously shown that asymptotically, there are 1.07427\cdot n^{-3/2} \cdot 2.35467^n many saturated structures for a sequence of length n.
Edit intent: fluency
Original: We study the situation of an investor-producer who can trade on a financial market in continuous time and can transform some assets into others by means of a discrete time production system, in order to price and hedge derivatives on produced goods.
Revised: We study the situation of an agent who can trade on a financial market in continuous time and can transform some assets into others by means of a discrete time production system, in order to price and hedge derivatives on produced goods.
Edit intent: clarity
Original: We study the situation of an investor-producer who can trade on a financial market in continuous time and can transform some assets into others by means of a discrete time production system, in order to price and hedge derivatives on produced goods.
Revised: We study the situation of an investor-producer who can trade on a financial market and can also transform some assets into others by means of a discrete time production system, in order to price and hedge derivatives on produced goods.
Edit intent: clarity
Original: We study the situation of an investor-producer who can trade on a financial market in continuous time and can transform some assets into others by means of a discrete time production system, in order to price and hedge derivatives on produced goods.
Revised: We study the situation of an investor-producer who can trade on a financial market in continuous time and can transform some assets into others by means of a production system, in order to price and hedge derivatives on produced goods.
Edit intent: clarity
Original:  We introduce the flexible concept of conditional sure profit along the idea of the no sure profit condition of Rasonyi (2009) and show that it allows one to provide a closedness property for the set of super-hedgeable claims in a very general  setting.
Revised:  We introduce the generic concept of conditional sure profit along the idea of the no sure profit condition of Rasonyi (2009) and show that it allows one to provide a closedness property for the set of super-hedgeable claims in a very general setting.
Edit intent: clarity
Original:  We introduce the flexible concept of conditional sure profit along the idea of the no sure profit condition of Rasonyi (2009) and show that it allows one to provide a closedness property for the set of super-hedgeable claims in a very general  setting.
Revised:  We introduce the flexible concept of conditional sure profit along the idea of the no sure profit condition of R\`asonyi (2009) and show that it allows one to provide a closedness property for the set of super-hedgeable claims in a very general setting.
Edit intent: fluency
Original:  We introduce the flexible concept of conditional sure profit along the idea of the no sure profit condition of Rasonyi (2009) and show that it allows one to provide a closedness property for the set of super-hedgeable claims in a very general  setting.
Revised:  We introduce the flexible concept of conditional sure profit along the idea of the no sure profit condition of Rasonyi (2009) . The condition allows one to provide a closedness property for the set of super-hedgeable claims in a very general setting.
Edit intent: coherence
Original:  We introduce the flexible concept of conditional sure profit along the idea of the no sure profit condition of Rasonyi (2009) and show that it allows one to provide a closedness property for the set of super-hedgeable claims in a very general  setting.
Revised:  We introduce the flexible concept of conditional sure profit along the idea of the no sure profit condition of Rasonyi (2009) and show that it allows one to provide a closedness property for the set of super-hedgeable claims in a very general financial setting.
Edit intent: clarity
Original: We solve four intertwined problems, motivated by mathematical finance, concerning degenerate-parabolic partial differential operators and degenerate diffusion processes. First, we consider a parabolic partial differential equation on a half-space whose coefficients are suitably Holder continuous and allowed to grow linearly in the spatial variable and which becomes degenerate along the boundary of the half-space.
Revised: We solve four intertwined problems, motivated by mathematical finance, we consider a parabolic partial differential equation on a half-space whose coefficients are suitably Holder continuous and allowed to grow linearly in the spatial variable and which becomes degenerate along the boundary of the half-space.
Edit intent: clarity
Original:  First, we consider a parabolic partial differential equation on a half-space whose coefficients are suitably Holder continuous and allowed to grow linearly in the spatial variable and which becomes degenerate along the boundary of the half-space.
Revised:  First, we consider a parabolic partial differential equation on a half-space whose coefficients are suitably Holder continuous and allowed to grow linearly in the spatial variable and which become degenerate along the boundary of the half-space.
Edit intent: fluency