scholarly journals Stochastic interest model driven by compound Poisson process and Brownian motion with applications in life contingencies

2018 ◽  
Vol 2 (1) ◽  
pp. 246-260 ◽  
Author(s):  
Shilong Li ◽  
◽  
Xia Zhao ◽  
Chuancun Yin ◽  
Zhiyue Huang ◽  
...  
Keyword(s):  
Brownian Motion ◽  
Poisson Process ◽  
Compound Poisson Process ◽  
Compound Poisson ◽  
Model Driven ◽  
And Brownian Motion ◽  
Stochastic Interest ◽  
Interest Model

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 Stochastic Interest Model Based on Compound Poisson Process and Applications in Actuarial Science

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Shilong Li ◽  
Chuancun Yin ◽  
Xia Zhao ◽  
Hongshuai Dai
Keyword(s):  
Interest Rates ◽  
Poisson Process ◽  
Compound Poisson Process ◽  
Compound Poisson ◽  
New Class ◽  
Interest Force ◽  
Validity Condition ◽  
Interest Model ◽  
Force Of Interest ◽  
Life Annuities

Considering stochastic behavior of interest rates in financial market, we construct a new class of interest models based on compound Poisson process. Different from the references, this paper describes the randomness of interest rates by modeling the force of interest with Poisson random jumps directly. To solve the problem in calculation of accumulated interest force function, one important integral technique is employed. And a conception called the critical value is introduced to investigate the validity condition of this new model. We also discuss actuarial present values of several life annuities under this new interest model. Simulations are done to illustrate the theoretical results and the effect of parameters in interest model on actuarial present values is also analyzed.

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