scholarly journals Insider Trading with Memory under Random Deadline

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Kai Xiao ◽  
Yonghui Zhou
Keyword(s):  
Numerical Simulation ◽  
Insider Trading ◽  
Continuous Time ◽  
Fixed Time ◽  
Necessary Condition ◽  
Noise Traders ◽  
Filtering Theory ◽  
Optimal Trading ◽  
Asset Value ◽  
With Memory

In this paper, we study a model of continuous-time insider trading in which noise traders have some memories and the trading stops at a random deadline. By a filtering theory on fractional Brownian motion and the stochastic maximum principle, we obtain a necessary condition of the insider’s optimal strategy, an equation satisfied. It shows that when the volatility of noise traders is constant and the noise traders’ memories become weaker and weaker, the optimal trading intensity and the corresponding residual information tend to those, respectively, when noise traders have no any memory. And, numerical simulation illustrates that if both the trading intensity of the insider and the volatility of noise trades are independent of trading time, the insider’s expected profit is always lower than that when the asset value is disclosed at a finite fixed time; this is because the trading time ahead is a random deadline which yields the loss of the insider’s information.

scholarly journals Continuous-Time Insider Trading with Risk-Neutral Insider under Imperfect Observation

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Yonghui Zhou ◽  
Guanglong Zhuang ◽  
Kai Xiao
Keyword(s):  
Insider Trading ◽  
Continuous Time ◽  
Imperfect Information ◽  
Complete Information ◽  
Market Depth ◽  
Asset Value ◽  
Risk Neutral ◽  
Maximal Profit ◽  
Expectation Theory ◽  
Open Question

A model of insider trading in continuous time in which a risk-neutral insider possesses long-lived imperfect information on a risk asset is studied. By conditional expectation theory and filtering theory, we turn it into a model with insider knowing complete information about the asset with a revised risky value and deduce its linear Bayesian equilibrium consisting of optimal insider trading strategy and semistrong pricing rule. It shows that, in the equilibrium, as the degree of insider observing the signal of the risky asset value is more and more accurate, market depth, trading intensity, and residual information are all decreasing and the total expectation profit of the insider is increasing and that the information about the asset value incorporated into the equilibrium price, which has nothing to do with the volatility of noise trades, is increasing as time goes by, but not all information of asset value is incorporated into the price in the final disclosed time due to the incompleteness of insider’s observation, though the market depth is still a time-independent constant. Some simulations are illustrated to show these features. However, it is an open question of how to make maximal profit if the insider is risk-averse.

The formation and evolution of a diffusive interface

1997 ◽  
Vol 331 ◽  
pp. 199-229 ◽  
Author(s):  
M. JEROEN MOLEMAKER ◽  
HENK A. DIJKSTRA
Keyword(s):  
Numerical Simulation ◽  
Mixed Layer ◽  
Numerical Results ◽  
Necessary Condition ◽  
Mixing Efficiency ◽  
Final Thickness ◽  
Formation And Evolution ◽  
Diffusive Interface ◽  
The Moment ◽  
Energy Balances

The formation and evolution of a diffusive interface in a stable salt-stratified layer cooled from above is studied in a two-dimensional geometry by direct numerical simulation. For a typical example with realistic parameters, the evolution of the flow is computed up to the moment where three layers can be distinguished. Focus is on the development of the first mixed layer. The convective velocity scaling as proposed by Hunt (1984) and previously proposed expressions for the interfacial heat flux (Huppert 1971; Fernando 1989a) are shown to correspond well with the results of the simulation. The evolution of the first layer can be well described by an entrainment relation based on a local balance between kinetic and potential energy with mixing efficiency γ. The new entrainment relation is shown to fit the numerical results well and an interpretation of γ in terms of the overall energy balances of the flow is given.Previously, two rival mechanisms have been proposed that determine the final thickness of the first layer (Turner 1968; Fernando 1987). One of the distinguishing features of both mechanisms is whether a transition in entrainment regime – as the first layer develops – is a necessary condition for the mixed layer to stop growing. Another is the presence of a buoyancy jump over the interface before substantial convection in the second layer occurs. From the numerical results, we find a significant buoyancy jump even before the thermal boundary layer ahead of the first layer becomes unstable. Moreover, the convective activity in the second layer is too small to be able to stop the growth of the first layer. We therefore favour the view proposed by Fernando (1987) that a transition in entrainment regime determines the thickness of the first layer. Following this, a new one-dimensional model of layer formation is proposed. Important expressions within this model are verified using the results of the numerical simulation. The model contains two constants which are determined from the numerical results. The results of the new model fit experimental results quite well and the parameter dependence of the thickness of the first layer is not sensitive to the values of the two constants.

Consensus Problem of Singular Multi-Agent Systems with Continuous-Time and Fixed Topology

2013 ◽  
Vol 278-280 ◽  
pp. 1687-1691
Author(s):  
Tong Qiang Jiang ◽  
Jia Wei He ◽  
Yan Ping Gao
Keyword(s):  
Continuous Time ◽  
Spanning Tree ◽  
Undirected Graph ◽  
Necessary Condition ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent ◽  
Fixed Topology ◽  
The Stability ◽  
Sufficient And Necessary Condition

The consensus problems of two situations for singular multi-agent systems with fixed topology are discussed: directed graph without spanning tree and the disconnected undirected graph. A sufficient and necessary condition is obtained by applying the stability theory and the system is reachable asymptotically. But for normal systems, this can’t occur in upper two situations. Finally a simulation example is provided to verify the effectiveness of our theoretical result.

scholarly journals An error-based active disturbance rejection control with memory structure

2020 ◽  
pp. 002029402091521 ◽  
Author(s):  
Sen Chen ◽  
Zhixiang Chen ◽  
Zhiliang Zhao
Keyword(s):  
Disturbance Rejection ◽  
Reference Signal ◽  
Memory Structure ◽  
Necessary Condition ◽  
Control Input ◽  
Active Disturbance Rejection Control ◽  
Active Disturbance Rejection ◽  
Disturbance Rejection Control ◽  
Input Gain ◽  
With Memory

The paper studies the control problem for nonlinear uncertain systems with the situation that only the current reference signal is available. By constructing a memory structure to save the previous reference signals, a novel error-based active disturbance rejection control with an approximation for the second-order derivative of reference signal is proposed. The transient performance of the proposed method is rigorously studied, which implies the high consistence of the closed-loop system. More importantly, to attain the satisfactory tracking performance, the necessary condition for nominal control input gain is quantitatively investigated. Furthermore, the superiority of the proposed method is illuminated by contrastively evaluating the sizes of the total disturbance and its derivative. The proposed method can alleviate the burden of the estimation and compensation for total disturbance. Finally, the experiment for a manipulator platform shows the effectiveness of the proposed method.

scholarly journals Non-Linear Macroeconomic Models of Growth with Memory

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2078 ◽  
Author(s):  
Vasily E. Tarasov
Keyword(s):  
Economic Growth ◽  
Differential Equations ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Continuous Time ◽  
Non Linear ◽  
Standard Models ◽  
Fractional Differential ◽  
Derivatives Of ◽  
With Memory

In this article, two well-known standard models with continuous time, which are proposed by two Nobel laureates in economics, Robert M. Solow and Robert E. Lucas, are generalized. The continuous time standard models of economic growth do not account for memory effects. Mathematically, this is due to the fact that these models describe equations with derivatives of integer orders. These derivatives are determined by the properties of the function in an infinitely small neighborhood of the considered time. In this article, we proposed two non-linear models of economic growth with memory, for which equations are derived and solutions of these equations are obtained. In the differential equations of these models, instead of the derivative of integer order, fractional derivatives of non-integer order are used, which allow describing long memory with power-law fading. Exact solutions for these non-linear fractional differential equations are obtained. The purpose of this article is to study the influence of memory effects on the rate of economic growth using the proposed simple models with memory as examples. As the methods of this study, exact solutions of fractional differential equations of the proposed models are used. We prove that the effects of memory can significantly (several times) change the growth rate, when other parameters of the model are unchanged.

scholarly journals Noise Characterization: Keeping Reduction Based Per-turbed Quantum Walk Search Optimal

2019 ◽  
Vol 198 ◽  
pp. 00001
Author(s):  
Chen-Fu Chiang ◽  
Chang-Yu Hsieh
Keyword(s):  
Invariant Subspace ◽  
Continuous Time ◽  
Quantum Walk ◽  
Coupling Factor ◽  
Necessary Condition ◽  
Subspace Method ◽  
Noise Distribution ◽  
Noisy Environment ◽  
Time Quantum ◽  
Noise Characterization

In a recent work by Novo et al. (Sci. Rep. 5, 13304, 2015), the invariant subspace method was applied to the study of continuous-time quantum walk (CTQW). In this work, we adopt the aforementioned method to investigate the optimality of a perturbed quantum walk search of a marked element in a noisy environment on various graphs. We formulate the necessary condition of the noise distribution in the system such that the invariant subspace method remains effective and efficient. Based on the noise, we further formulate how to set the appropriate coupling factor to preserve the optimality of the quantum walker.

INSIDER TRADING IN CONTINUOUS TIME

2006 ◽  
Author(s):  
EMILIO BARUCCI ◽  
ROBERTO MONTE ◽  
BARBARA TRIVELLATO
Keyword(s):  
Insider Trading ◽  
Continuous Time

scholarly journals On a Model for the Storage of Files on a Hardware: Statistics at a Fixed Time and Asymptotic Regimes

2009 ◽  
Vol 2009 ◽  
pp. 1-24
Author(s):  
Vincent Bansaye
Keyword(s):  
Point Process ◽  
Real Line ◽  
Continuous Time ◽  
Poisson Point Process ◽  
Fixed Time ◽  
The Real ◽  
Parking Problem ◽  
The Right

We consider a version in continuous time of the parking problem of Knuth. Files arrive following a Poisson point process and are stored on a hardware identified with the real line, in the closest free portions at the right of the arrival location. We specify the distribution of the space of unoccupied locations at a fixed time and give asymptotic regimes when the hardware is becoming full.

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