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In modern markets, limit order traders can no longer be characterized as passive traders, which has led some researchers to argue that limit orders, rather than trades, are the informational unit in today's markets. If this is tru...
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In modern markets, limit order traders can no longer be characterized as passive traders, which has led some researchers to argue that limit orders, rather than trades, are the informational unit in today's markets. If this is true, measures such as order imbalance, which uses signed trades and captures the information from liquidity demanders, may not be as valid as they once were. We calculate two measures of limit order imbalance and examine the relation between limit order imbalances and returns. We find evidence that limit order imbalances explain returns, but conclude that traditional order imbalance has more explanatory power. Thus, our results suggest that limit orders have not trumped trades as the informational unit in today's markets.
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Let X_1, ..., X_n be independent exponential random variables with respective hazard rates λ_1,, ..., λ_n, and Y_x,...,Y_nbe i.i.d. exponential random variables with common hazard rate λ. It is proved that X_(2:n), the second o...
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Let X_1, ..., X_n be independent exponential random variables with respective hazard rates λ_1,, ..., λ_n, and Y_x,...,Y_nbe i.i.d. exponential random variables with common hazard rate λ. It is proved that X_(2:n), the second order statistic from X_l, ..., X_n, is larger than Y_(2:n), the second order statistic from Y_1 ... ,Y_n, with respect to the right spread order if and only if λ≥(2n-1)/(n(n-1)(∑_(i=1~n 1/∧_i -(n-1)/∧(1)))) with ∧(1) = ∑_(i=1)~n λ_i and ∧_i = ∧(1) - λ_i, and X_(2:n) is smaller than Y_(2:n) with respect to the right spread order if and only if λ≤∑_(i=1)~n λ_i-max_(1≤i≤n)λ_i/n-1 Further, the case with proportional decreasing hazard rate is also studied, and the results obtained here form nice extensions to some corresponding ones known in the literature.
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We investigate additive transformations on the space of real or complex matrices that are monotone with respect to any admissible partial order relation. A complete characterization of these transformations is obtained. In the rea...
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We investigate additive transformations on the space of real or complex matrices that are monotone with respect to any admissible partial order relation. A complete characterization of these transformations is obtained. In the real case, we show that such transformations are linear and that all nonzero monotone transformations are bijective. As a corollary, we characterize all additive transformations that are monotone with respect to certain classical matrix order relations, in particular, with respect to the Drazin order, left and right *-orders, and the diamond order.
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In this paper, we extend the existing empirical evidence on the relationship between the state of the limit order book (LOB) and order choice. Our contribution is twofold: first, we propose a sequential ordered probit (SOP) model ...
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In this paper, we extend the existing empirical evidence on the relationship between the state of the limit order book (LOB) and order choice. Our contribution is twofold: first, we propose a sequential ordered probit (SOP) model which allows studying patient and impatient traders' choices separately; second, we consider two pieces of LOB information, the best quotes and the book beyond the best quotes. We find that both pieces of LOB information explain the degree of patience of an incoming trader and, afterwards, its order choice. Nonetheless, the best quotes concentrate most of the explanatory power of the LOB. The shape of the book beyond the best quotes is crucial in explaining the aggressiveness of patient (limit order) traders, while impatient (market order) traders base their decisions primarily on the best quotes. Patient traders' choices depend more on the state of the LOB on the same side of the market, while impatient traders mostly look at the state of the LOB on the opposite side. The aggressiveness of both types of traders augments with the inside spread. However, patient (impatient) traders submit more (less) aggressive limit (market) orders when the depth of the own (opposite) best quote and the length of the own (opposite) side of the book increase. We also find that higher depth away from the best ask (bid) quote may signal that this quote is 'too low (high)', causing incoming impatient buyers (sellers) to be more aggressive and incoming patient sellers (buyers) to be more conservative.
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In this paper, the sample range from a heterogeneous exponential sample is shown to be larger than that from a homogeneous exponential sample in the sense of the star ordering. Then, by using this result, some equivalent character...
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In this paper, the sample range from a heterogeneous exponential sample is shown to be larger than that from a homogeneous exponential sample in the sense of the star ordering. Then, by using this result, some equivalent characterizations of stochastic comparisons of sample ranges with respect to various stochastic orders are established. In this process, two open problems mentioned in Mao and Hu (2010) [16] are solved. The main results established here extend and strengthen several known results in the literature including those of Khaledi and Kochar (2000) [8], Zhao and Li (2009) [22] and Genest etal. (2009) [7].
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Two constructions have been given previously of the Wallman orderedcompactification ω_0X of a T_1-ordered, convex ordered topological space(X, τ, ≤).Bothof those papers note that ω_0X is T_1,but need not be T_1-ordered. Using ...
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Two constructions have been given previously of the Wallman orderedcompactification ω_0X of a T_1-ordered, convex ordered topological space(X, τ, ≤).Bothof those papers note that ω_0X is T_1,but need not be T_1-ordered. Using this as onemotivation, we propose a new version of Ti-ordered, called Tr-ordered, which has theproperty that the Wallman ordered compactification of a T_1~K-ordered topological spaceis Tr-ordered. We also discuss the Ro-ordered (R_0~K-ordered) property, defined so thatan ordered topological space is Ti-ordered (T_1~K-ordered) if and only if it is To-orderedand R_0-ordered (R_0~K -ordered).
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We will show that all subspaces of well-ordered spaces are orderable, and we will characterize the well-orderability of subspaces of well-ordered spaces.
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A partial latin square P of order n is ann x n array with entries from the set {1, 2, ... , n}such that each symbol is used at most once in eachrow and at most once in each column. If every cell ofthe array is filled we call P a l...
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A partial latin square P of order n is ann x n array with entries from the set {1, 2, ... , n}such that each symbol is used at most once in eachrow and at most once in each column. If every cell ofthe array is filled we call P a latin square. A partiallatin square P of order n is said to be avoidable ifthere exists a latin square L of order n such that Pand L are disjoint. That is, corresponding cells of Pand L contain different entries. In this note we showthat, with the trivial exception of the latin square oforder 1, every partial latin square of order congruentto 1 modulo 4 is avoidable.
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Abstract We introduce a concept of a quasi proximate order which is a generalization of a proximate order and allows us to study efficiently analytic functions whose order and lower order of growth are different. We prove an exist...
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Abstract We introduce a concept of a quasi proximate order which is a generalization of a proximate order and allows us to study efficiently analytic functions whose order and lower order of growth are different. We prove an existence theorem for a quasi proximate order, i.e. a counterpart of Valiron’s theorem for a proximate order. As applications, we generalize and complement some results of M. Cartwright and C. N. Linden on asymptotic behavior of analytic functions in the unit disc.
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We define the (n, i, f)-tube orders, which include interval orders, trapezoid orders, triangle orders, weak orders, order dimension n, and interval-order-dimension n as special cases. We investigate some basic properties of (n, i,...
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We define the (n, i, f)-tube orders, which include interval orders, trapezoid orders, triangle orders, weak orders, order dimension n, and interval-order-dimension n as special cases. We investigate some basic properties of (n, i, f)-tube orders, and begin classifying them by containment.
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