This paper presents a model to describe the dynamic trading process in limit order book.By studying the dynamic pattern of execution probabilities of limit orders with both time and the depth of limit order book,the a...This paper presents a model to describe the dynamic trading process in limit order book.By studying the dynamic pattern of execution probabilities of limit orders with both time and the depth of limit order book,the authors conclude with the following properties:Arrival rates of market buy orders increase as the depth of buy queue in the book increases and decrease as the depth of sell queue increases,and vice versa;similar regularities for the arrival rate of market sell orders;both the arrival rate of market buy order and market sell orders increase as the depth of both sides in the book increases by the same amount.Furthermore,the authors describe more detailed temporary and permanent effects of the market depth on the arrival rates of orders.展开更多
This work studies the constrained optimal execution problem with a random market depth in the limit order market.Motivated from the real trading activities,our execution model considers the execution bounds and allows...This work studies the constrained optimal execution problem with a random market depth in the limit order market.Motivated from the real trading activities,our execution model considers the execution bounds and allows the random market depth to be statistically correlated in different periods.Usually,it is difficult to achieve the analytical solution for this class of constrained dynamic decision problem.Thanks to the special structure of this model,by applying the proposed state separation theorem and dynamic programming,we successfully obtain the analytical execution policy.The revealed policy is of feedback nature.Examples are provided to illustrate our solution methods.Simulation results demonstrate the advantages of our model comparing with the classical execution policy.展开更多
A model of continuous-time insider trading in which a risk-neutral in-sider possesses two imperfect correlated signals of a risky asset is studied.By conditional expectation theory and filtering theory,we first establ...A model of continuous-time insider trading in which a risk-neutral in-sider possesses two imperfect correlated signals of a risky asset is studied.By conditional expectation theory and filtering theory,we first establish three lemmas:normal corre-lation,equivalent pricing and equivalent profit,which can guarantee to turn our model into a model with insider knowing full information.Then we investigate the impact of the two correlated signals on the market equilibrium consisting of optimal insider trading strategy and semi-strong pricing rule.It shows that in the equilibrium,(1)the market depth is constant over time;(2)if the two noisy signals are not linerly correlated,then all private information of the insider is incorporated into prices in the end while the whole information on the asset value can not incorporated into prices in the end;(3)if the two noisy signals are linear correlated such that the insider can infer the whole information of the asset value,then our model turns into a model with insider knowing full information;(4)if the two noisy signals are the same then the total ex ant profit of the insider is increasing with the noise decreasing,while down to O as the noise going up to infinity;(5)if the two noisy signals are not linear correlated then with one noisy signal fixed,the total ex ante profit of the insider is single-peaked with a unique minimum with respect to the other noisy signal value,and furthermore as the noisy value going to O it gets its maximum,the profit in the case that the real value is observed.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.71371024,71371023Fundamental Research Funds for the Central Universities under Grant No.ZZ1319
文摘This paper presents a model to describe the dynamic trading process in limit order book.By studying the dynamic pattern of execution probabilities of limit orders with both time and the depth of limit order book,the authors conclude with the following properties:Arrival rates of market buy orders increase as the depth of buy queue in the book increases and decrease as the depth of sell queue increases,and vice versa;similar regularities for the arrival rate of market sell orders;both the arrival rate of market buy order and market sell orders increase as the depth of both sides in the book increases by the same amount.Furthermore,the authors describe more detailed temporary and permanent effects of the market depth on the arrival rates of orders.
基金This research is partially supported by the National Natural Science Foundation of China(No.61573244).
文摘This work studies the constrained optimal execution problem with a random market depth in the limit order market.Motivated from the real trading activities,our execution model considers the execution bounds and allows the random market depth to be statistically correlated in different periods.Usually,it is difficult to achieve the analytical solution for this class of constrained dynamic decision problem.Thanks to the special structure of this model,by applying the proposed state separation theorem and dynamic programming,we successfully obtain the analytical execution policy.The revealed policy is of feedback nature.Examples are provided to illustrate our solution methods.Simulation results demonstrate the advantages of our model comparing with the classical execution policy.
文摘A model of continuous-time insider trading in which a risk-neutral in-sider possesses two imperfect correlated signals of a risky asset is studied.By conditional expectation theory and filtering theory,we first establish three lemmas:normal corre-lation,equivalent pricing and equivalent profit,which can guarantee to turn our model into a model with insider knowing full information.Then we investigate the impact of the two correlated signals on the market equilibrium consisting of optimal insider trading strategy and semi-strong pricing rule.It shows that in the equilibrium,(1)the market depth is constant over time;(2)if the two noisy signals are not linerly correlated,then all private information of the insider is incorporated into prices in the end while the whole information on the asset value can not incorporated into prices in the end;(3)if the two noisy signals are linear correlated such that the insider can infer the whole information of the asset value,then our model turns into a model with insider knowing full information;(4)if the two noisy signals are the same then the total ex ant profit of the insider is increasing with the noise decreasing,while down to O as the noise going up to infinity;(5)if the two noisy signals are not linear correlated then with one noisy signal fixed,the total ex ante profit of the insider is single-peaked with a unique minimum with respect to the other noisy signal value,and furthermore as the noisy value going to O it gets its maximum,the profit in the case that the real value is observed.
