scholarly journals On the Dynamics of Semimartingales with Two Reflecting Barriers

2013 ◽  
Vol 50 (3) ◽  
pp. 671-685 ◽  
Author(s):  
Mats Pihlsgård ◽  
Peter W. Glynn
Keyword(s):  
Structural Properties ◽  
Explicit Construction ◽  
General Relationship ◽  
Local Times ◽  
Stochastic Integrals ◽  
Reflecting Barriers ◽  
Additional Assumptions

We consider a semimartingale X which is reflected at an upper barrier T and a lower barrier S, where S and T are also semimartingales such that T is bounded away from S. First, we present an explicit construction of the reflected process. Then we derive a relationship in terms of stochastic integrals linking the reflected process and the local times at the respective barriers to X, S, and T. This result reveals the fundamental structural properties of the reflection mechanism. We also present a few results showing how the general relationship simplifies under additional assumptions on X, S, and T, e.g. if we take X, S, and T to be independent martingales (which satisfy some extra technical conditions).

On the Dynamics of Semimartingales with Two Reflecting Barriers

2013 ◽  
Vol 50 (03) ◽  
pp. 671-685 ◽  
Author(s):  
Mats Pihlsgård ◽  
Peter W. Glynn
Keyword(s):  
Structural Properties ◽  
Explicit Construction ◽  
General Relationship ◽  
Local Times ◽  
Stochastic Integrals ◽  
Reflecting Barriers ◽  
Additional Assumptions

We consider a semimartingaleXwhich is reflected at an upper barrierTand a lower barrierS, whereSandTare also semimartingales such thatTis bounded away fromS. First, we present an explicit construction of the reflected process. Then we derive a relationship in terms of stochastic integrals linking the reflected process and the local times at the respective barriers toX,S, andT. This result reveals the fundamental structural properties of the reflection mechanism. We also present a few results showing how the general relationship simplifies under additional assumptions onX,S, andT, e.g. if we takeX,S, andTto be independent martingales (which satisfy some extra technical conditions).

Pricing via anticipative stochastic calculus

1994 ◽  
Vol 26 (04) ◽  
pp. 1006-1021
Author(s):  
Eckhard Platen ◽  
Rolando Rebolledo
Keyword(s):  
Structural Properties ◽  
General Model ◽  
Stochastic Calculus ◽  
Stochastic Equations ◽  
Stochastic Integrals ◽  
Derivative Securities

The paper proposes a general model for pricing of derivative securities. The underlying dynamics follows stochastic equations involving anticipative stochastic integrals. These equations are solved explicitly and structural properties of solutions are studied.

scholarly journals Markov-Modulated Brownian Motion with Two Reflecting Barriers

2010 ◽  
Vol 47 (04) ◽  
pp. 1034-1047 ◽  
Author(s):  
Jevgenijs Ivanovs
Keyword(s):  
Brownian Motion ◽  
Stationary Distribution ◽  
Simple Form ◽  
Transient Behavior ◽  
Local Times ◽  
Probabilistic Argument ◽  
Markov Modulated ◽  
Reflecting Barriers

We consider a Markov-modulated Brownian motion reflected to stay in a strip [0, B]. The stationary distribution of this process is known to have a simple form under some assumptions. We provide a short probabilistic argument leading to this result and explain its simplicity. Moreover, this argument allows for generalizations including the distribution of the reflected process at an independent, exponentially distributed epoch. Our second contribution concerns transient behavior of the model. We identify the joint law of the processes defining the model at inverse local times.

Pricing via anticipative stochastic calculus

1994 ◽  
Vol 26 (4) ◽  
pp. 1006-1021
Author(s):  
Eckhard Platen ◽  
Rolando Rebolledo
Keyword(s):  
Structural Properties ◽  
General Model ◽  
Stochastic Calculus ◽  
Stochastic Equations ◽  
Stochastic Integrals ◽  
Derivative Securities

The paper proposes a general model for pricing of derivative securities. The underlying dynamics follows stochastic equations involving anticipative stochastic integrals. These equations are solved explicitly and structural properties of solutions are studied.

scholarly journals Markov-Modulated Brownian Motion with Two Reflecting Barriers

2010 ◽  
Vol 47 (4) ◽  
pp. 1034-1047 ◽  
Author(s):  
Jevgenijs Ivanovs
Keyword(s):  
Brownian Motion ◽  
Stationary Distribution ◽  
Simple Form ◽  
Transient Behavior ◽  
Local Times ◽  
Probabilistic Argument ◽  
Markov Modulated ◽  
Reflecting Barriers

We consider a Markov-modulated Brownian motion reflected to stay in a strip [0, B]. The stationary distribution of this process is known to have a simple form under some assumptions. We provide a short probabilistic argument leading to this result and explain its simplicity. Moreover, this argument allows for generalizations including the distribution of the reflected process at an independent, exponentially distributed epoch. Our second contribution concerns transient behavior of the model. We identify the joint law of the processes defining the model at inverse local times.

Newborn's Preference for Faces

1996 ◽  
Vol 1 (3) ◽  
pp. 200-205 ◽  
Author(s):  
Carlo Umiltà ◽  
Francesca Simion ◽  
Eloisa Valenza
Keyword(s):  
Visual System ◽  
Structural Properties ◽  
Sensory Properties ◽  
Human Face ◽  
System Experiment ◽  
Face Experiment

Four experiments were aimed at elucidating some aspects of the preference for facelike patterns in newborns. Experiment 1 showed a preference for a stimulus whose components were located in the correct arrangement for a human face. Experiment 2 showed a preference for stimuli that had optimal sensory properties for the newborn visual system. Experiment 3 showed that babies directed their attention to a facelike pattern even when it was presented simultaneously with a non-facelike stimulus with optimal sensory properties. Experiment 4 showed the preference for facelike patterns in the temporal hemifield but not in the nasal hemifield. It was concluded that newborns' preference for facelike patterns reflects the activity of a subcortical system which is sensitive to the structural properties of the stimulus.

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