Stability of switched stochastic dynamical systems driven by brownian motion and Markov modulated compound Poisson process

2011 ◽  
Author(s):  
Ahmet Cetinkaya ◽  
Tomohisa Hayakawa
Keyword(s):  
Brownian Motion ◽  
Dynamical Systems ◽  
Poisson Process ◽  
Compound Poisson Process ◽  
Stochastic Dynamical Systems ◽  
Compound Poisson ◽  
Markov Modulated

The busy cycle of the reflected superposition of Brownian motion and a compound Poisson process

2001 ◽  
Vol 38 (1) ◽  
pp. 255-261 ◽  
Author(s):  
David Perry ◽  
Wolfgang Stadje
Keyword(s):  
Brownian Motion ◽  
Poisson Process ◽  
Closed Form ◽  
Queueing System ◽  
Heavy Traffic ◽  
Compound Poisson Process ◽  
Compound Poisson ◽  
Maximum Workload ◽  
Busy Cycle

We consider a reflected superposition of a Brownian motion and a compound Poisson process as a model for the workload process of a queueing system with two types of customers under heavy traffic. The distributions of the duration of a busy cycle and the maximum workload during a cycle are determined in closed form.

The first rendezvous time of Brownian motion and compound Poisson-type processes

2004 ◽  
Vol 41 (04) ◽  
pp. 1059-1070 ◽  
Author(s):  
D. Perry ◽  
W. Stadje ◽  
S. Zacks
Keyword(s):  
Brownian Motion ◽  
Stochastic Processes ◽  
Poisson Process ◽  
Compound Poisson Process ◽  
Reflected Brownian Motion ◽  
Compound Poisson ◽  
Brownian Motion With Drift ◽  
First Time ◽  
Random Jump ◽  
Poisson Type

The ‘rendezvous time’ of two stochastic processes is the first time at which they cross or hit each other. We consider such times for a Brownian motion with drift, starting at some positive level, and a compound Poisson process or a process with one random jump at some random time. We also ask whether a rendezvous takes place before the Brownian motion hits zero and, if so, at what time. These questions are answered in terms of Laplace transforms for the underlying distributions. The analogous problem for reflected Brownian motion is also studied.

The first rendezvous time of Brownian motion and compound Poisson-type processes

2004 ◽  
Vol 41 (4) ◽  
pp. 1059-1070 ◽  
Author(s):  
D. Perry ◽  
W. Stadje ◽  
S. Zacks
Keyword(s):  
Brownian Motion ◽  
Stochastic Processes ◽  
Poisson Process ◽  
Compound Poisson Process ◽  
Reflected Brownian Motion ◽  
Compound Poisson ◽  
Brownian Motion With Drift ◽  
First Time ◽  
Random Jump ◽  
Poisson Type

The ‘rendezvous time’ of two stochastic processes is the first time at which they cross or hit each other. We consider such times for a Brownian motion with drift, starting at some positive level, and a compound Poisson process or a process with one random jump at some random time. We also ask whether a rendezvous takes place before the Brownian motion hits zero and, if so, at what time. These questions are answered in terms of Laplace transforms for the underlying distributions. The analogous problem for reflected Brownian motion is also studied.

scholarly journals Hubungan Antara Brownian Motion (The Winner Process) dan Surplus Process

2012 ◽  
Vol 12 (1) ◽  
pp. 47
Author(s):  
Tohap Manurung
Keyword(s):  
Brownian Motion ◽  
Poisson Process ◽  
Wiener Process ◽  
Compound Poisson Process ◽  
Risk Process ◽  
Actuarial Science ◽  
Compound Poisson ◽  
Brownian Motion With Drift ◽  
Surplus Process ◽  
The Standard Model

HUBUNGAN ANTARA BROWNIAN MOTION (THE WIENER PROCESS) DAN SURPLUS PROCESS ABSTRAK Suatu analisis model continous-time menjadi cakupan yang akan dibahas dalam tulisan ini. Dengan demikian pengenalan proses stochastic akan sangat berperan. Dua proses akan di analisis yaitu proses compound Poisson dan Brownian motion. Proses compound Poisson sudah menjadi model standard untuk Ruin analysis dalam ilmu aktuaria. Sementara Brownian motion sangat berguna dalam teori keuangan modern dan juga dapat digunakan sebagai approksimasi untuk proses compound Poisson. Hal penting dalam tulisan ini adalah menujukkan bagaimana surplus process berdasarkan proses resiko compound Poisson dihubungkan dengan Brownian motion with Drift Process. Kata kunci: Brownian motion with Drift process, proses surplus, compound Poisson   RELATIONSHIP  BETWEEN  BROWNIAN MOTION (THE WIENER PROCESS) AND THE SURPLUS PROCESS ABSTRACT An analysis of continous-time models is covered in this paper. Thus, this requires an introduction to stochastic processes. Two processes are analyzed: the compound Poisson process and Brownian motion. The compound Poisson process has been the standard model for ruin analysis in actuarial science, while Brownian motion has found considerable use in modern financial theory and also can be used as an approximation to the compound Pisson process. The important thing is to show how the surplus process based on compound poisson risk process is related to Brownian motion with drift process. Keywords: Brownian motion with drift process, surplus process, compound Poisson

The busy cycle of the reflected superposition of Brownian motion and a compound Poisson process

2001 ◽  
Vol 38 (01) ◽  
pp. 255-261
Author(s):  
David Perry ◽  
Wolfgang Stadje
Keyword(s):  
Brownian Motion ◽  
Poisson Process ◽  
Closed Form ◽  
Queueing System ◽  
Heavy Traffic ◽  
Compound Poisson Process ◽  
Compound Poisson ◽  
Maximum Workload ◽  
Busy Cycle

We consider a reflected superposition of a Brownian motion and a compound Poisson process as a model for the workload process of a queueing system with two types of customers under heavy traffic. The distributions of the duration of a busy cycle and the maximum workload during a cycle are determined in closed form.

scholarly journals Large deviations for risk processes with reinsurance

2006 ◽  
Vol 43 (03) ◽  
pp. 713-728 ◽  
Author(s):  
Claudio Macci ◽  
Gabriele Stabile
Keyword(s):  
Large Deviations ◽  
Poisson Process ◽  
Large Deviation ◽  
Compound Poisson Process ◽  
Ruin Probabilities ◽  
Small Claim ◽  
Compound Poisson ◽  
Numerical Example ◽  
Markov Modulated ◽  
Risk Processes

We consider risk processes with reinsurance. A general family of reinsurance contracts is allowed, including proportional and excess-of-loss policies. Claim occurrence is regulated by a classical compound Poisson process or by a Markov-modulated compound Poisson process. We provide some large deviation results concerning these two risk processes in the small-claim case. Finally, we derive the so-called Lundberg estimate for the ruin probabilities and present a numerical example.

ASYMMETRIC INFORMATION IN A FINANCIAL MARKET WITH JUMPS

2000 ◽  
Vol 03 (04) ◽  
pp. 641-659 ◽  
Author(s):  
AXEL GRORUD
Keyword(s):  
Brownian Motion ◽  
Asymmetric Information ◽  
Poisson Process ◽  
Explicit Expression ◽  
Financial Market ◽  
Compound Poisson Process ◽  
Optimal Portfolio ◽  
Financial Strategy ◽  
Compound Poisson ◽  
Mouvement Brownien

This paper uses the enlargement of filtrations to analyze the financial strategy of an insider trader in a discontinuous time market where prices are driven by a Brownian motion and a compound Poisson process. We compare this strategy with that of a non-insider trader. The market is a chosen viable and complete; we can give an explicit expression of the optimal portfolio of the insider trader. On considère un marché financier dont les prix sont dirigés par un mouvement brownien et un processus de Poisson multivarié. Dans ce cadre le marché peut être complet et viable. Nous étudions la stratégie financière d'un agent qui a une information anticipant l'évolution du marché et nous la comparons un agent qui n'a pas cette information. La complétude du marché permet d'expliciter le portefeuille optimal de l'agent initié. Le grossissement de filtration permet de replacer une équation anticipante dans un cadre adapté.

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