scholarly journals Order Book Dynamics in Liquid Markets: Limit Theorems and Diffusion Approximations

2012 ◽  
Author(s):  
Rama Cont ◽  
Adrien de Larrard
Keyword(s):  
Limit Theorems ◽  
Order Book ◽  
Diffusion Approximations ◽  
And Diffusion

scholarly journals Diffusion approximations for randomly arriving expert opinions in a financial market with Gaussian drift

2021 ◽  
Vol 58 (1) ◽  
pp. 197-216 ◽  
Author(s):  
Jörn Sass ◽  
Dorothee Westphal ◽  
Ralf Wunderlich
Keyword(s):  
Stock Returns ◽  
Financial Market ◽  
Discrete Time ◽  
High Frequency ◽  
Utility Maximization ◽  
Limit Theorems ◽  
Approximate Solutions ◽  
Diffusion Approximations ◽  
Expert Opinions ◽  
Arrival Intensity

AbstractThis paper investigates a financial market where stock returns depend on an unobservable Gaussian mean reverting drift process. Information on the drift is obtained from returns and randomly arriving discrete-time expert opinions. Drift estimates are based on Kalman filter techniques. We study the asymptotic behavior of the filter for high-frequency experts with variances that grow linearly with the arrival intensity. The derived limit theorems state that the information provided by discrete-time expert opinions is asymptotically the same as that from observing a certain diffusion process. These diffusion approximations are extremely helpful for deriving simplified approximate solutions of utility maximization problems.

scholarly journals A review of the deterministic and diffusion approximations for stochastic chemical reaction networks

2018 ◽  
Vol 123 (2) ◽  
pp. 289-312 ◽  
Author(s):  
Pavel Mozgunov ◽  
Marco Beccuti ◽  
Andras Horvath ◽  
Thomas Jaki ◽  
Roberta Sirovich ◽  
...  
Keyword(s):  
Chemical Reaction ◽  
Chemical Reaction Networks ◽  
Reaction Networks ◽  
Diffusion Approximations ◽  
And Diffusion

scholarly journals DIFFUSION LIMITS FOR A MARKOV MODULATED BINOMIAL COUNTING PROCESS

2019 ◽  
Vol 34 (2) ◽  
pp. 235-257
Author(s):  
Peter Spreij ◽  
Jaap Storm
Keyword(s):  
Markov Chain ◽  
Markov Process ◽  
Regime Switching ◽  
Limit Theorems ◽  
Counting Process ◽  
Limit Behavior ◽  
Diffusion Approximations ◽  
Default Rate ◽  
Markov Modulated ◽  
Rapid Switching

In this paper, we study limit behavior for a Markov-modulated binomial counting process, also called a binomial counting process under regime switching. Such a process naturally appears in the context of credit risk when multiple obligors are present. Markov-modulation takes place when the failure/default rate of each individual obligor depends on an underlying Markov chain. The limit behavior under consideration occurs when the number of obligors increases unboundedly, and/or by accelerating the modulating Markov process, called rapid switching. We establish diffusion approximations, obtained by application of (semi)martingale central limit theorems. Depending on the specific circumstances, different approximations are found.

Sojourns and extremes of a diffusion process on a fixed interval

1982 ◽  
Vol 14 (4) ◽  
pp. 811-832 ◽  
Author(s):  
Simeon M. Berman
Keyword(s):  
Diffusion Process ◽  
Lebesgue Measure ◽  
Stationary Distribution ◽  
Real Line ◽  
Diffusion Coefficients ◽  
Limit Theorems ◽  
Random Variable ◽  
Fixed Interval ◽  
The Real ◽  
And Diffusion

Let X(t), , be an Ito diffusion process on the real line. For u > 0 and t > 0, let Lt(u) be the Lebesgue measure of the set . Limit theorems are obtained for (i) the distribution of Lt(u) for u → ∞and fixed t, and (ii) the tail of the distribution of the random variable max[0, t]X(s). The conditions on the process are stated in terms of the drift and diffusion coefficients. These conditions imply the existence of a stationary distribution for the process.

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