wanyu/IteraTeR_full_sent huggingface dataset:
Original:  In this paper we considered the efficient hedging for European call option in general Black-Scholes model dX_t=X_t(m(t)dt+\sigma (t)dw(t)) with time-varying drift and volatility coefficients and in fractional Black-Scholes model dX_t=X_t( mdt+\sigma dB _H(t)  ) with constant coefficients.
Revised:  In this paper we considered the efficient hedging for European call option in general Black-Scholes model dX_t=X_t(m(t)dt+\sigma (t)dw(t)) with time-varying drift and volatility coefficients and in fractional Black-Scholes model dX_t=X_t( mdt+\sigma dB _H(t) +mdt ) with constant coefficients.
Edit intent: meaning-changed
Original: Most decision theories  including expected utility theory, rank dependent utility theory and the cumulative prospect theory  assume that investors are only interested in the distribution of returns and not about the states of the economy in which income is received.
Revised: Most decision theories , including expected utility theory, rank dependent utility theory and the cumulative prospect theory assume that investors are only interested in the distribution of returns and not about the states of the economy in which income is received.
Edit intent: fluency
Original: Most decision theories  including expected utility theory, rank dependent utility theory and the cumulative prospect theory  assume that investors are only interested in the distribution of returns and not about the states of the economy in which income is received.
Revised: Most decision theories including expected utility theory, rank dependent utility theory and the cumulative prospect theory , assume that investors are only interested in the distribution of returns and not about the states of the economy in which income is received.
Edit intent: fluency
Original:  We introduce a framework for portfolio selection that permits to deal with state-dependent preferences . We are able to characterize optimal payoffs in explicit form.
Revised:  We introduce a framework for portfolio selection that permits to deal with state-dependent preferences can be accommodated. Specifically, we assume that investors care about the distribution of final wealth and its interaction with some benchmark. In this context, we are able to characterize optimal payoffs in explicit form.
Edit intent: meaning-changed
Original:   To validate our approach we employ the Gillespiemethod to generate benchmark data. The numerical simulation shows that the data produced by both methods agree quite well .
Revised:  To validate our approach we employ Gillespie's stochastic simulation algorithm (SSA) to generate (forward) benchmark data, according to predefined gene network models. Numerical simulations show that the BSDE method is able to correctly infer the protein level distributions that preceded a known final condition, obtained originally from the forward SSA. This makes the BSDE method a powerful systems biology tool for time reversed simulations, allowing, for example, the assessment of the biological conditions (e.g. protein concentrations) that preceded an experimentally measured event of interest (e.g. mitosis, apoptosis, etc.) .
Edit intent: meaning-changed
Original: We present a careful analysis of  a set of effects that lead to significant biases in the estimation of the branching ratio n that quantifies the degree of endogeneity of how much past events trigger future events.
Revised: We present a careful analysis of possible issues of the application of the self-excited Hawkes process to high-frequency financial data and carefully analyze a set of effects that lead to significant biases in the estimation of the branching ratio n that quantifies the degree of endogeneity of how much past events trigger future events.
Edit intent: meaning-changed
Original: We present a careful analysis of  a set of effects that lead to significant biases in the estimation of the branching ratio n that quantifies the degree of endogeneity of how much past events trigger future events.
Revised: We present a careful analysis of a set of effects that lead to significant biases in the estimation of the "criticality index" n that quantifies the degree of endogeneity of how much past events trigger future events.
Edit intent: meaning-changed
Original:  We report (i) evidence of strong upward biases on the estimation of n when using power law memory kernels in the presence of a few outliers, (ii) strong effects on nresulting from the form of the regularization part of the power law kernel, (iii) strong edge effects on the estimated n when using power law kernels, and (iv) the need for an exhaustive search of the absolute maximum of the log-likelihood function due to its complicated shape.
Revised:  We report a number of model biases that are intrinsic to the estimation of n when using power law memory kernels in the presence of a few outliers, (ii) strong effects on nresulting from the form of the regularization part of the power law kernel, (iii) strong edge effects on the estimated n when using power law kernels, and (iv) the need for an exhaustive search of the absolute maximum of the log-likelihood function due to its complicated shape.
Edit intent: clarity
Original:  We report (i) evidence of strong upward biases on the estimation of n when using power law memory kernels in the presence of a few outliers, (ii) strong effects on nresulting from the form of the regularization part of the power law kernel, (iii) strong edge effects on the estimated n when using power law kernels, and (iv) the need for an exhaustive search of the absolute maximum of the log-likelihood function due to its complicated shape.
Revised:  We report (i) evidence of strong upward biases on the estimation of brnaching ratio (n) when using power law kernels, and (iv) the need for an exhaustive search of the absolute maximum of the log-likelihood function due to its complicated shape.
Edit intent: clarity
Original:  We report (i) evidence of strong upward biases on the estimation of n when using power law memory kernels in the presence of a few outliers, (ii) strong effects on nresulting from the form of the regularization part of the power law kernel, (iii) strong edge effects on the estimated n when using power law kernels, and (iv) the need for an exhaustive search of the absolute maximum of the log-likelihood function due to its complicated shape. Moreover, we demonstrate that the calibration of the Hawkes process on mixtures of pure Poisson process with changes of regime leads to completely spurious apparent critical values for the branching ratio (n = 1) while the true value is actually n=0.
Revised:  We report (i) evidence of strong upward biases on the estimation of n when using power law memory kernels in the presence of a few outliers, (ii) strong effects on nresulting from the form of the regularization part of the power law kernel, (iii) strong edge effects on the estimated n when using power law memory kernels. We demonstrate that the calibration of the Hawkes process on mixtures of pure Poisson process with changes of regime leads to completely spurious apparent critical values for the branching ratio (n = 1) while the true value is actually n=0.
Edit intent: coherence
Original:  Moreover, we demonstrate that the calibration of the Hawkes process on mixtures of pure Poisson process with changes of regime leads to completely spurious apparent critical values for the branching ratio (n = 1) while the true value is actually n=0.
Revised:  Moreover, we demonstrate that the calibration of the Hawkes process on mixtures of pure Poisson process with changes of regime leads to completely spurious apparent critical values for the branching ratio (n \simeq 1) while the true value is actually n=0.
Edit intent: meaning-changed
Original:  In this respect, because the above effects are plaguing their analyses, the claim by Hardiman, Bercot and Bouchaud (2013) that financial market have been continuously functioning at or close to criticality (n = 1) cannot be supported.
Revised:  In this respect, because the above effects are plaguing their analyses, the claim by Hardiman, Bercot and Bouchaud (2013) that financial market have been continuously functioning at or close to criticality (n \simeq 1) cannot be supported.
Edit intent: meaning-changed
Original: We present a careful analysis of possible issues of the application of the self-excited Hawkes process to high-frequency financial data and carefully analyze a set of effects that lead to significant biases in the estimation of the "criticality index" n that quantifies the degree of endogeneity of how much past events trigger future events.
Revised: We present a careful analysis of possible issues on the application of the self-excited Hawkes process to high-frequency financial data and carefully analyze a set of effects that lead to significant biases in the estimation of the "criticality index" n that quantifies the degree of endogeneity of how much past events trigger future events.
Edit intent: fluency
Original: We present a careful analysis of possible issues of the application of the self-excited Hawkes process to high-frequency financial data and carefully analyze a set of effects that lead to significant biases in the estimation of the "criticality index" n that quantifies the degree of endogeneity of how much past events trigger future events.
Revised: We present a careful analysis of possible issues of the application of the self-excited Hawkes process to high-frequency financial data . We carefully analyze a set of effects that lead to significant biases in the estimation of the "criticality index" n that quantifies the degree of endogeneity of how much past events trigger future events.
Edit intent: fluency
Original: We present a careful analysis of possible issues of the application of the self-excited Hawkes process to high-frequency financial data and carefully analyze a set of effects that lead to significant biases in the estimation of the "criticality index" n that quantifies the degree of endogeneity of how much past events trigger future events.
Revised: We present a careful analysis of possible issues of the application of the self-excited Hawkes process to high-frequency financial data and carefully analyze a set of effects leading to significant biases in the estimation of the "criticality index" n that quantifies the degree of endogeneity of how much past events trigger future events.
Edit intent: fluency
Original:  We demonstrate that the calibration of the Hawkes process on mixtures of pure Poisson process with changes of regime leads to completely spurious apparent critical values for the branching ratio (n \simeq 1) while the true value is actually n=0.
Revised:  We demonstrate that the calibration of the Hawkes process on mixtures of pure Poisson process with changes of regime leads to completely spurious apparent critical values for the branching ratio (n ~ 1) while the true value is actually n=0.
Edit intent: meaning-changed
Original:  In this respect, because the above effects are plaguing their analyses, the claim by Hardiman, Bercot and Bouchaud (2013) that financial market have been continuously functioning at or close to criticality (n \simeq 1) cannot be supported.
Revised:  In this respect, because the above effects are plaguing their analyses, the claim by Hardiman, Bercot and Bouchaud (2013) that financial market have been continuously functioning at or close to criticality (n ~ 1) cannot be supported.
Edit intent: meaning-changed
Original:  The prospect agents make actions based on their reactions to gains and losses, and as a consequence of the feedback effect, a relationship between the agents' trading behavior and the price fluctuations is constructed, which explains the implied volatility smile and skewness phenomena observed in actual market.
Revised:  The prospect agents make actions based on their reactions to gains and losses, and as a consequence of the feedback effect, a relationship between the agents' trading behavior and the price fluctuations is constructed, which explains the implied volatility skew and smile observed in actual market.
Edit intent: clarity
Original:  When the diffusion coefficient is locally Holder continuous with some exponent in (0, 1], the stochastic solution  is shown to be a classical solution . A comparison theorem for the Cauchy problem is also proved, without the\ge  linear growth condition on the diffusion coefficient.
Revised:  When the diffusion coefficient is locally Holder continuous with some exponent in (0, 1], the stochastic solution is shown to be a classical solution to the Cauchy problem is also proved, without the\ge linear growth condition on the diffusion coefficient.
Edit intent: clarity
Original:  Moreover, we establish the equivalence: the stochastic solution is the unique classical solution to the Cauchy problem if, and only if, a comparison theorem holds. For the case where the stochastic solution may not be smooth, we characterize it as a limit of smooth  stochastic solutions associated with some approximating Cauchy problems .
Revised:  Moreover, we establish the equivalence: the stochastic solution is not smooth stochastic solutions associated with some approximating Cauchy problems .
Edit intent: clarity
Original:  For the case where the stochastic solution may not be smooth, we characterize it as a limit of smooth  stochastic solutions associated with some approximating Cauchy problems .
Revised:  For the case where the stochastic solution may not be smooth, we characterize it as a limit of smooth , it is characterized as the limit of an approximating smooth stochastic solutions associated with some approximating Cauchy problems .
Edit intent: coherence
Original:  For the case where the stochastic solution may not be smooth, we characterize it as a limit of smooth  stochastic solutions associated with some approximating Cauchy problems .
Revised:  For the case where the stochastic solution may not be smooth, we characterize it as a limit of smooth stochastic solutions . In deriving the main results, we discover a new, probabilistic proof of Kotani's criterion for martingality of a one-dimensional diffusion in natural scale .
Edit intent: meaning-changed
Original:  To illustrate the approach we consider the problem of using datato predict the conditional distribution of the near future of a stationary, ergodic time series and compare it with probabilistic approaches based on first fitting a model. We believe our reduction of this regression problem for streams to a linear problem is clean, systematic, and efficient in minimizing the effective dimensionality.
Revised:  We believe that the insight provided by this paper will provide additional tool in the toolbox for studying sequential data. Our reduction of this regression problem for streams to a linear problem is clean, systematic, and efficient in minimizing the effective dimensionality.
Edit intent: clarity
Original:  Although the approach is non-parametric, it presents itself in computationally tractable and flexible restricted forms in examples we considered . Popular techniques in time series analysis such as AR, ARCH and GARCH can be seen to be special cases of our approach, but it is not clear if they are always the best or most informative choices .
Revised:  In examples we considered, we use the autoregressive calibration (AR approach) and Gaussian processes regression (GP approach) as two benchmarks, our approach presents itself in computationally tractable and flexible restricted forms in examples we considered . Popular techniques in time series analysis such as AR, ARCH and GARCH can be seen to be special cases of our approach, but it is not clear if they are always the best or most informative choices .
Edit intent: meaning-changed
Original:  Although the approach is non-parametric, it presents itself in computationally tractable and flexible restricted forms in examples we considered . Popular techniques in time series analysis such as AR, ARCH and GARCH can be seen to be special cases of our approach, but it is not clear if they are always the best or most informative choices .
Revised:  Although the approach is non-parametric, it presents itself in a more robust and flexible restricted forms in examples we considered . Popular techniques in time series analysis such as AR, ARCH and GARCH can be seen to be special cases of our approach, but it is not clear if they are always the best or most informative choices .
Edit intent: clarity
Original:  Although the approach is non-parametric, it presents itself in computationally tractable and flexible restricted forms in examples we considered . Popular techniques in time series analysis such as AR, ARCH and GARCH can be seen to be special cases of our approach, but it is not clear if they are always the best or most informative choices .
Revised:  Although the approach is non-parametric, it presents itself in computationally tractable and flexible restricted form compared with the AR approach, while as a non-parametric approach, it achieves similar accuracy to the GP approach with much lower computational cost especially when the sample size is large . Popular techniques in time series analysis such as AR, ARCH and GARCH can be seen to be special cases of our approach, but it is not clear if they are always the best or most informative choices .
Edit intent: meaning-changed
Original:  Although the approach is non-parametric, it presents itself in computationally tractable and flexible restricted forms in examples we considered . Popular techniques in time series analysis such as AR, ARCH and GARCH can be seen to be special cases of our approach, but it is not clear if they are always the best or most informative choices .
Revised:  Although the approach is non-parametric, it presents itself in computationally tractable and flexible restricted forms in examples we considered . Popular techniques in time series analysis such as AR, ARCH and GARCH can be incorporated to our model .
Edit intent: clarity
Original: Regression analysis aims to use observational data from multiple observations to develop a functional relationship relating explanatory variables to response variables, which is important for much of modern statistics, and econometrics, and also the field of machine learning. In this paper, we consider the special case where the explanatory variable is a stream of information, and the  response is also potentially a stream.
Revised: We bring the theory of rough paths to the study of non-parametric statistics on streamed data. We discuss the problem of regression where the input variable is a stream of information, and the response is also potentially a stream.
Edit intent: meaning-changed
Original:  We provide an approach based on identifying carefully chosen features of the streamwhich allows linear regression to be used to characterise the functional relationship between  explanatory variables and the conditional distribution of the response;
Revised:  A certain graded feature set of a stream, known in the rough path literature as the signature, has a universality that allows formally, linear regression to be used to characterise the functional relationship between explanatory variables and the conditional distribution of the response;
Edit intent: meaning-changed
Original:  We provide an approach based on identifying carefully chosen features of the streamwhich allows linear regression to be used to characterise the functional relationship between  explanatory variables and the conditional distribution of the response; the methods used to develop and justify this approach, such as the signature of a streamand the shuffle product of tensors, are standard tools in the theory of rough pathsand seem appropriate in this context of regression as well and provide a surprisingly unified and non-parametric approach.
Revised:  We provide an approach based on identifying carefully chosen features of the streamwhich allows linear regression to be used to characterise the functional relationship between explanatory variables and the conditional distribution of the dependent response. This approach, via linear regression on the signature of a streamand the shuffle product of tensors, are standard tools in the theory of rough pathsand seem appropriate in this context of regression as well and provide a surprisingly unified and non-parametric approach.
Edit intent: clarity
Original:  the methods used to develop and justify this approach, such as the signature of a streamand the shuffle product of tensors, are standard tools in the theory of rough pathsand seem appropriate in this context of regression as well and provide a surprisingly unified and non-parametric approach. We believe that the insight provided by this paper will provide additional tool in the toolbox for studying sequential data. Our reductionof this regression problem for streams to a linear problem is clean, systematic, and efficient in minimizing the effective dimensionality. The clear gradation of finite dimensional approximations increases its usefulness. In examples we considered, we use the autoregressive calibration (AR approach) and Gaussian processes regression (GP approach) as two benchmarks, our approach presents itself in a more robust and flexible restricted form compared with the AR approach, while as a non-parametric approach, it achieves similar accuracy to the GP approach with much lower computational cost especially when the sample size is large . Popular techniques in time series analysis such as AR, ARCH and GARCH can be incorporated to our model .
Revised:  the methods used to develop and justify this approach, such as the signature of the stream, is almost totally general, and yet it still allows explicit computation. The grading allows truncation of the feature set and so leads to an efficient local description for streams (rough paths). In the statistical context this method offers potentially significant, even transformational dimension reduction. By way of illustration, our approach is applied to stationary time series including the familiar AR model and ARCH model. In the numerical examples we examined, our predictions achieve similar accuracy to the GP approach with much lower computational cost especially when the sample size is large . Popular techniques in time series analysis such as AR, ARCH and GARCH can be incorporated to our model .
Edit intent: coherence
Original:  and Gaussian processes regression (GP approach) as two benchmarks, our approach presents itself in a more robust and flexible restricted form compared with the AR approach, while as a non-parametric approach, it achieves similar accuracy to the GP approach with much lower computational cost especially when the sample size is large . Popular techniques in time series analysis such as AR, ARCH and GARCH can be incorporated to our model .
Revised:  and Gaussian processes regression (GP approach) as two benchmarks, our approach presents itself in a more robust and flexible restricted form compared with the AR approach, while as a non-parametric approach, it achieves similar accuracy to the Gaussian Process (GP) approach with much lower computational cost especially when the sample size is large . Popular techniques in time series analysis such as AR, ARCH and GARCH can be incorporated to our model .
Edit intent: fluency
Original:  and Gaussian processes regression (GP approach) as two benchmarks, our approach presents itself in a more robust and flexible restricted form compared with the AR approach, while as a non-parametric approach, it achieves similar accuracy to the GP approach with much lower computational cost especially when the sample size is large . Popular techniques in time series analysis such as AR, ARCH and GARCH can be incorporated to our model .
Revised:  and Gaussian processes regression (GP approach) as two benchmarks, our approach presents itself in a more robust and flexible restricted form compared with the AR approach, while as a non-parametric approach, it achieves similar accuracy to the GP approach with much lower computational cost especially when the sample size is large .
Edit intent: coherence