Coherent-state representations for functionals of the wiener process and the poisson process

1994 ◽  
Vol 77 (4) ◽  
pp. 22-33
Author(s):  
Hisanao Ogura
Keyword(s):  
Coherent State ◽  
Poisson Process ◽  
Wiener Process

Wiener and Poisson process regularization for coherent‐state path integrals

1993 ◽  
Vol 34 (9) ◽  
pp. 3867-3877 ◽  
Author(s):  
Robert Alicki ◽  
John R. Klauder
Keyword(s):  
Coherent State ◽  
Poisson Process ◽  
Path Integrals ◽  
State Path

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

scholarly journals Optimal Dividends in the Dual Model with Diffusion

2008 ◽  
Vol 38 (02) ◽  
pp. 653-667 ◽  
Author(s):  
Benjamin Avanzi ◽  
Hans U. Gerber
Keyword(s):  
Poisson Process ◽  
Wiener Process ◽  
Compound Poisson Process ◽  
Dual Model ◽  
Optimal Dividends ◽  
Sample Paths ◽  
Optimal Dividend ◽  
The Individual ◽  
A Company ◽  
Poisson Parameter

In the dual model, the surplus of a company is a Lévy process with sample paths that are skip-free downwards. In this paper, the aggregate gains process is the sum of a shifted compound Poisson process and an independent Wiener process. By means of Laplace transforms, it is shown how the expectation of the discounted dividends until ruin can be calculated, if a barrier strategy is applied, and how the optimal dividend barrier can be determined. Conditions for optimality are discussed and several numerical illustrations are given. Furthermore, a family of models is analysed where the individual gain amount distribution is rescaled and compensated by a change of the Poisson parameter.

scholarly journals Optimization under the PMλ,τ policy of a finite dam with both continuous and jumpwise inputs

2005 ◽  
Vol 42 (2) ◽  
pp. 587-594
Author(s):  
Kyung Eun Lim ◽  
Jee Seon Baek ◽  
Eui Yong Lee
Keyword(s):  
Poisson Process ◽  
Wiener Process ◽  
Release Rate ◽  
Average Cost ◽  
Long Run ◽  
Random Jumps ◽  
Finite Dam

We consider a finite dam under the policy, where the input of water is formed by a Wiener process subject to random jumps arriving according to a Poisson process. The long-run average cost per unit time is obtained after assigning costs to the changes of release rate, a reward to each unit of output, and a penalty that is a function of the level of water in the reservoir.

scholarly journals Optimal Dividends in the Dual Model with Diffusion

2008 ◽  
Vol 38 (2) ◽  
pp. 653-667 ◽  
Author(s):  
Benjamin Avanzi ◽  
Hans U. Gerber
Keyword(s):  
Poisson Process ◽  
Wiener Process ◽  
Compound Poisson Process ◽  
Dual Model ◽  
Optimal Dividends ◽  
Sample Paths ◽  
Optimal Dividend ◽  
The Individual ◽  
A Company ◽  
Poisson Parameter

In the dual model, the surplus of a company is a Lévy process with sample paths that are skip-free downwards. In this paper, the aggregate gains process is the sum of a shifted compound Poisson process and an independent Wiener process. By means of Laplace transforms, it is shown how the expectation of the discounted dividends until ruin can be calculated, if a barrier strategy is applied, and how the optimal dividend barrier can be determined. Conditions for optimality are discussed and several numerical illustrations are given. Furthermore, a family of models is analysed where the individual gain amount distribution is rescaled and compensated by a change of the Poisson parameter.

scholarly journals Optimization under the P M λ,τ policy of a finite dam with both continuous and jumpwise inputs

2005 ◽  
Vol 42 (02) ◽  
pp. 587-594
Author(s):  
Kyung Eun Lim ◽  
Jee Seon Baek ◽  
Eui Yong Lee
Keyword(s):  
Poisson Process ◽  
Wiener Process ◽  
Release Rate ◽  
Average Cost ◽  
Long Run ◽  
Random Jumps ◽  
Finite Dam

We consider a finite dam under the policy, where the input of water is formed by a Wiener process subject to random jumps arriving according to a Poisson process. The long-run average cost per unit time is obtained after assigning costs to the changes of release rate, a reward to each unit of output, and a penalty that is a function of the level of water in the reservoir.

Lectures on the Poisson Process

2017 ◽  
Author(s):  
Günter Last ◽  
Mathew Penrose
Keyword(s):  
Poisson Process
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