wanyu/IteraTeR_full_sent huggingface dataset:
Original:  We show that the logarithmic trading price process is a renewal reward process, and that, under a suitable scaling, this renewal reward process converges to a standard Brownian motion \to \to0 . Finally, we develop a GBM asymptotic model for trading prices, and derive a simple and effective prediction formula .
Revised:  We show that the logarithmic trading price process is a renewal reward process, and that, under a suitable scaling, this renewal reward process converges to a standard Brownian motion as \delta\to \to0 . Finally, we develop a GBM asymptotic model for trading prices, and derive a simple and effective prediction formula .
Edit intent: meaning-changed
Original:  We show that the logarithmic trading price process is a renewal reward process, and that, under a suitable scaling, this renewal reward process converges to a standard Brownian motion \to \to0 . Finally, we develop a GBM asymptotic model for trading prices, and derive a simple and effective prediction formula .
Revised:  We show that the logarithmic trading price process is a renewal reward process, and that, under a suitable scaling, this renewal reward process converges to a standard Brownian motion \to 0. We also prove that the modified ask and bid processes approach the original bouncing GBMs as \delta\to0 . Finally, we develop a GBM asymptotic model for trading prices, and derive a simple and effective prediction formula .
Edit intent: meaning-changed
Original:  We show that the logarithmic trading price process is a renewal reward process, and that, under a suitable scaling, this renewal reward process converges to a standard Brownian motion \to \to0 . Finally, we develop a GBM asymptotic model for trading prices, and derive a simple and effective prediction formula .
Revised:  We show that the logarithmic trading price process is a renewal reward process, and that, under a suitable scaling, this renewal reward process converges to a standard Brownian motion \to \to0 . Finally, we derive a simple and effective prediction formula .
Edit intent: meaning-changed
Original:  We show that the logarithmic trading price process is a renewal reward process, and that, under a suitable scaling, this renewal reward process converges to a standard Brownian motion \to \to0 . Finally, we develop a GBM asymptotic model for trading prices, and derive a simple and effective prediction formula . We illustrate the effectiveness of the prediction methods with an example using real stock price data.
Revised:  We show that the logarithmic trading price process is a renewal reward process, and that, under a suitable scaling, this renewal reward process converges to a standard Brownian motion \to \to0 . Finally, we develop a GBM asymptotic model for trading prices, and derive a simple and effective prediction formula for trading prices, and illustrate the effectiveness of the prediction methods with an example using real stock price data.
Edit intent: fluency
Original:  To this end, the paradigm of a pre-determined num\'eraire is abandoned in favour of a symmetrical point of view where all assets have equal priority. This approach yields novel versions of the Fundamental Theorems of Asset Pricing, which clarify and extend non-classical pricing formulas used in the financial community. Furthermore, conditioning on non-devaluation, each asset can serve as proper num\'eraire and a classical no-arbitrage condition can be formulated.
Revised:  Conditioning on non-devaluation, each asset can serve as proper num\'eraire and a classical no-arbitrage condition can be formulated.
Edit intent: coherence
Original: In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic forward investment performance processes (power, exponential and logarithmic) .
Revised: In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic (power, exponential and logarithmic) .
Edit intent: clarity
Original: In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic forward investment performance processes (power, exponential and logarithmic) . We develop a connection with ergodic and infinite horizon quadratic BSDE, and with a risk-sensitive control problem.
Revised: In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic forward investment performance processes (power, exponential and logarithmic) forward performance processes in factor-form using ergodic BSDE. We also develop a connection with ergodic and infinite horizon quadratic BSDE, and with a risk-sensitive control problem.
Edit intent: meaning-changed
Original:  We develop a connection with ergodic and infinite horizon quadratic BSDE, and with a risk-sensitive control problem. We also develop a connection, for large trading horizons, with a family of traditional homothetic value function processes  .
Revised:  We develop a connection with ergodic and infinite horizon quadratic BSDE, and with a risk-sensitive optimization. In addition, we develop a connection, for large trading horizons, with a family of traditional homothetic value function processes .
Edit intent: clarity
Original: Tail risk measures such as the conditional value-at-risk are useful in the context of portfolio selection for quantifying potential losses in worst cases. However, for scenario-based problems these are problematic: because the value of a tail risk measure only depends on a small subset of the support of the distribution of asset returns, traditional scenario based methods, which spread scenarios evenly across the whole support of the distribution, yield very unstable solutions unless we use a very large number scenarios .
Revised: Scenario generation is the construction of a discrete random vector to represent parameters of uncertain values in a stochastic program. Most approaches to scenario generation are distribution-driven, that is, they attempt to construct a random vector which captures well in a probabilistic sense the uncertainty. On the other hand, a problem-driven approach may be able to exploit the structure of a problem to provide a more concise representation of the uncertainty. There have been only a few problem-driven approaches proposed, and these have been heuristic in nature .
Edit intent: meaning-changed
Original:  In this paper we propose a problem-driven scenario generation methodology for portfolio selection problems using a tail risk measure where the the asset returns have elliptical or near-elliptical distribution.
Revised:  In this paper we propose what is, as far as we are aware, the first analytic approach to problem-driven scenario generation methodology for portfolio selection problems using a tail risk measure where the the asset returns have elliptical or near-elliptical distribution.
Edit intent: meaning-changed
Original:  In this paper we propose a problem-driven scenario generation methodology for portfolio selection problems using a tail risk measure where the the asset returns have elliptical or near-elliptical distribution. Our approach in effect prioritizes the construction of scenarios in the areas of the distributionwhich correspond to the tail losses of feasible portfolios. The methodology is shown to work particularly well when the distribution of assets returns are positively correlated and heavy-tailed, and the performance is shown to improve as we tighten the constraints on feasible assets .
Revised:  In this paper we propose a problem-driven scenario generation methodology for portfolio selection problems using a tail risk measure , such as conditional value-at-risk. Since tail risk measures only depend on the upper tail of a distribution, standard methods of scenario generation, which typically spread there scenarios evenly across the support of the solution, struggle to adequately represent tail risk well .
Edit intent: meaning-changed
Original: Scenario generation is the construction of a discrete random vector to represent parameters of uncertain values in a stochastic program. Most approaches to scenario generation are distribution-driven, that is, they attempt to construct a random vector which captures well in a probabilistic sense the uncertainty. On the other hand, a problem-driven approach may be able to exploit the structure of a problem to provide a more concise representation of the uncertainty. There have been only a few problem-driven approaches proposed, and these have been heuristic in nature.
Edit intent: coherence
Original:  In this paper we propose what is, as far as we are aware, the first analytic approach to problem-driven scenario generation . This approach applies to stochastic programs with a tail risk measure, such as conditional value-at-risk.
Revised:  In this paper we propose what is, as far as we are aware, the first analytic approach to problem-driven scenario generation approach to the single-period portfolio selection problem which use tail risk measures such as conditional value-at-risk.
Edit intent: meaning-changed
Original:  Since tail risk measures only depend on the upper tail of a distribution , standard methods of scenario generation, which typically spread there scenarios evenly across the  support of the solution, struggle to adequately represent tail risk well .
Revised:  Tail risk measures are useful for quantifying potential losses in worst cases. However, for scenario-based problems these are problematic: because the value of a tail risk measure only depends on a small subset of the support of the distribution of asset returns, traditional scenario based methods, which spread scenarios evenly across the support of the solution, struggle to adequately represent tail risk well .
Edit intent: meaning-changed
Original:  Since tail risk measures only depend on the upper tail of a distribution , standard methods of scenario generation, which typically spread there scenarios evenly across the  support of the solution, struggle to adequately represent tail risk well .
Revised:  Since tail risk measures only depend on the upper tail of a distribution , standard methods of scenario generation, which typically spread there scenarios evenly across the whole support of the solution, struggle to adequately represent tail risk well .
Edit intent: clarity
Original:  Since tail risk measures only depend on the upper tail of a distribution , standard methods of scenario generation, which typically spread there scenarios evenly across the  support of the solution, struggle to adequately represent tail risk well .
Revised:  Since tail risk measures only depend on the upper tail of a distribution , standard methods of scenario generation, which typically spread there scenarios evenly across the support of the distribution, yield very unstable solutions unless we use a very large number of scenarios. The proposed approach works by prioritizing the construction of scenarios in the areas of a probability distribution which correspond to the tail losses of feasible portfolios. The proposed approach can be applied to difficult instances of the portfolio selection problem characterized by high-dimensions, non-elliptical distributions of asset returns, and the presence of integer variables. It is also observed that the methodology works better as the feasible set of portfolios becomes more constrained. Based on this fact, a heuristic algorithm based on the sample average approximation method is proposed. This algorithm works by adding artificial constraints to the problem which are gradually tightened, allowing one to telescope onto high quality solutions .
Edit intent: meaning-changed
Original:  We present a simple biophysical model , where chromosomes are described in terms of folding of a chromatin sequence with alternating blocks of fibers with different thickness. We demonstrate that chromosomes undergo prominent conformational changes when the two fibers form separate domains.
Revised:  We present a simple biophysical model , where chromosomes are described in terms of folding of a chromatin sequence with alternating blocks of fibers with different thicknesses and flexibilities, and we use it to study the influence of sequence disorder on chromosome behaviors in space and time. By employing extensive computer simulations,we thus demonstrate that chromosomes undergo prominent conformational changes when the two fibers form separate domains.
Edit intent: meaning-changed
Original:  We demonstrate that chromosomes undergo prominent conformational changes when the two fibers form separate domains. Conversely, when small stretches of the thinner fiber are randomly distributed, they act as impurities and conformational changes can be observed only at small length and time scales. Our results bring a limit to the possibility of detecting variations in the behavior of chromosomes due to chromatin modifications, and suggest that the debate whether chromosomes expand upon transcription, which is fueled by conflicting experimental observations, can be reconciled by examining how transcribed loci are distributed. Finally, to validate our conclusions, we compare our results to experimental FISH data .
Revised:  We demonstrate that chromosomes undergo noticeable conformational changes only on length-scales smaller than 10^5 basepairs and time-scales shorter than a few seconds, and we suggest there might exist effective upper bounds to the detection of chromosome URLanization in eukaryotes. We prove the relevance of our framework by modeling recent experimental FISH data on murine chromosomes .
Edit intent: clarity
Original: We introduce an optimal measure transformation problem for zero coupon bond prices based on dynamic relative entropy of probability measures. In the default-free case we prove the equivalence of the optimal measure transformation problem and an optimal stochastic control problem of Gombani and Runggaldier (Math. Financ. 23(4):659-686, 2013) for bond prices. We also consider the optimal measure transformation problem for defaultable bonds, futures contracts, and forward contracts.
Revised: We introduce the entropic measure transform (EMT) problem for a general process and prove the existence of a unique optimal measure characterizing the solution. The density process of the optimal measure transformation problem for defaultable bonds, futures contracts, and forward contracts.
Edit intent: meaning-changed
Original:  We also consider the optimal measure transformation problem for defaultable bonds, futures contracts, and forward contracts. We provide financial interpretations of the optimal measure transformation problems in terms of the  maximization of returns subject to a relative entropy penalty term.
Revised:  We also consider the optimal measure is characterized using a semimartingale BSDE under general conditions. The EMT is used to reinterpret the conditional entropic risk-measure and to obtain a convenient formula for the conditional expectation of a process which admits an affine representation under a related measure. The entropic measure transform is then used provide a new characterization of defaultable bond prices, forward prices, and futures prices when the asset is driven by a jump diffusion. The characterization of these pricing problems in terms of the maximization of returns subject to a relative entropy penalty term.
Edit intent: meaning-changed
Original:  We provide financial interpretations of the optimal measure transformation problems in terms of the  maximization of returns subject to a relative entropy penalty term. In general the solution of the optimal measure transformation problem is characterized by the solution of certain decoupled nonlinear forward-backward stochastic differential equations (FBSDEs) .
Revised:  We provide financial interpretations of the optimal measure transformation problems in terms of the maximization of returns subject to a penalty for removing financial risk as expressed through the aggregate relative entropy .
Edit intent: meaning-changed
Original:  In specific classes of models we show how these FBSDEs can be solved explicitly or at least numerically .
Revised:  The EMT is shown to extend the optimal stochastic control characterization of default-free bond prices of Gombani and Runggaldier (Math. Financ. 23(4):659-686, 2013). These methods are illustrated numerically with an example in the defaultable bond setting .
Edit intent: meaning-changed
Original:  The MAPK cascade (Raf-MEK-ERK pathway) is used as an illustrative example which demon- strates how the computational modularity provided by the bond graph approach avoids the errors associated with assuming irreversible Michaelis-Menten kinetics and emphasises the necessity for a power supply to support behavioural modularity in signalling networks .
Revised:  The MAPK cascade (Raf-MEK-ERK pathway) is used as an illustrative example .
Edit intent: coherence
Original:  In this paper we present a class of risk measures composed of coherent risk measures with generalized deviation measures . Based on the  Limitedness axiom, we prove that this set is a sub-class of coherent risk measures.
Revised: The definition of risk is based on two main concepts: the possibility of loss, and variability. In this paper we present a class of risk measures composed of coherent risk measures with generalized deviation measures . Based on the Limitedness axiom, we prove that this set is a sub-class of coherent risk measures.
Edit intent: meaning-changed
Original:  In this paper we present a class of risk measures composed of coherent risk measures with generalized deviation measures . Based on the  Limitedness axiom, we prove that this set is a sub-class of coherent risk measures.
Revised:  In this paper we present a composition of risk and deviation measures, which capt these two concepts . Based on the Limitedness axiom, we prove that this set is a sub-class of coherent risk measures.
Edit intent: meaning-changed
Original:  In this paper we present a class of risk measures composed of coherent risk measures with generalized deviation measures . Based on the  Limitedness axiom, we prove that this set is a sub-class of coherent risk measures.
Revised:  In this paper we present a class of risk measures composed of coherent risk measures with generalized deviation measures . Based on the proposed Limitedness axiom, we prove that this set is a sub-class of coherent risk measures.
Edit intent: meaning-changed
Original:  In this paper we present a class of risk measures composed of coherent risk measures with generalized deviation measures . Based on the  Limitedness axiom, we prove that this set is a sub-class of coherent risk measures. We present extensions of this result for the case of convex or co-monotone coherent risk measures.
Revised:  In this paper we present a class of risk measures composed of coherent risk measures with generalized deviation measures . Based on the Limitedness axiom, we prove that this set is a sub-class of coherent , convex or co-monotone coherent risk measures.
Edit intent: clarity
Original:  We present extensions of this result for the case of convex or co-monotone coherent risk measures. Under this perspective, we propose a specific formulation that generates, from any coherent measure, a generalized deviation based on the dispersion of results worse than it, which leads to a very interesting risk measure. Moreover, we present some examples of risk measures that lie in our proposed class .
Revised:  We present extensions of this result for the case of convex or co-monotone risk measures, conform the properties of the two components .
Edit intent: meaning-changed
Original:  Based on the proposed Limitedness axiom, we prove that this set is a sub-class of coherent, convex or co-monotone risk measures, conform the properties of the two components  .
Revised:  Based on the proposed Limitedness axiom, we prove that this set is a sub-class of coherent, convex or co-monotone risk measures, conform the properties of the two components . We also provide examples of known and new risk measures constructed under this framework, in order to highlight the importance of our approach, specially the role of the Limitedness axiom .
Edit intent: meaning-changed
Original:  Based on the proposed Limitedness axiom, we prove that this composition is a coherent, convex or co-monotone risk measure, conform properties of the two components .
Revised:  Based on the proposed Limitedness axiom, we prove that this composition is a coherent, convex or co-monotone risk measure, conform properties of the two components , is a coherent risk measure. Similar results for the cases of convex and co-monotone risk measures are exposed.
Edit intent: meaning-changed
Original: In this paper, we focus on model-free pricing and robust hedging of options depending on the local time , consistent with Vanilla options. This problem is classically approached by means of the Skorokhod embedding problem (SEP), which consists in representing a given probability on the real line as the distribution of a Brownian motion stopped at a chosen stopping time .
Revised: In this paper, we focus on model-free pricing and robust hedging of options depending on the local time when one or more marginals of the underlying price process are known .
Edit intent: meaning-changed
Original:  By using the stochastic control approach initiated by Galichon, Henry-Labordere and Touzi, we recover the optimal hedging strategies and the corresponding prices given by Vallois ' embeddings to the SEP . Furthermore, we extend the analysis to the two-marginal case .
Revised:  By using the stochastic control approach initiated in Galichon, Henry-Labord\`ere and Touzi, we recover the optimal hedging strategies and the corresponding prices given by Vallois ' embeddings to the SEP . Furthermore, we extend the analysis to the two-marginal case .
Edit intent: fluency
Original:  By using the stochastic control approach initiated by Galichon, Henry-Labordere and Touzi, we recover the optimal hedging strategies and the corresponding prices given by Vallois ' embeddings to the SEP . Furthermore, we extend the analysis to the two-marginal case .
Revised:  By using the stochastic control approach initiated by Galichon, Henry-Labordere and Touzi, we identify the optimal hedging strategies and the corresponding prices given by Vallois ' embeddings to the SEP . Furthermore, we extend the analysis to the two-marginal case .
Edit intent: clarity
Original:  By using the stochastic control approach initiated by Galichon, Henry-Labordere and Touzi, we recover the optimal hedging strategies and the corresponding prices given by Vallois ' embeddings to the SEP . Furthermore, we extend the analysis to the two-marginal case .
Revised:  By using the stochastic control approach initiated by Galichon, Henry-Labordere and Touzi, we recover the optimal hedging strategies and the corresponding prices in the one-marginal case. As a by-product, we recover the property that the Vallois solutions to the Skorokhod embedding problem (SEP) maximize and minimize the expectation of any convex function of the local time . Furthermore, we extend the analysis to the two-marginal case .
Edit intent: meaning-changed