create new Wiener process

はじめる前に
新機能一覧
Maple ワークシートの作成
Mapleワークシートを共有
Maple ウィンドウのカスタマイズ
Maple システムのカスタマイズ
コネクティビティ
Mathematics
数学
- テンソル解析
- パッケージ
- ファンクションアドバイザ
- ベキ級数
- ベクトル解析
- 不活性関数
- 代数
- 因数分解と方程式解法
- 基本数学
- 基本的な注意事項
- 変分法
- 変換
- 幾何
- 微分代数方程式
- 微分幾何学
- 微分方程式
- 微積分
- 数
- 数値計算
- 数学関数
- 数論
- 最適化
- 特殊関数
- 統計
- 線形代数
- 群論
- 評価
- 論理
- 過去のパッケージ
- 金融
  - はじめに
  - キャッシュフロー分析
  - パーソナルファイナンス
  - ラティス法
  - 日付計算
  - 短期料率モデル
  - 確率過程
  - 金利
  - 金融商品
  - 概要
- 離散数学
- piecewise examples
- グラフ電卓
- 区分関数
物理
プログラミング
グラフィックス
Student パッケージ
Science and Engineering
科学・エンジニアリング
アプリケーションと例題
リファレンス
システム
MapleSim
MapleSim ツールボックス
MapleSim ヘルプ
Tasks
Toolboxes
エラーメッセージガイド
マニュアル
数学アプリ

Finance[WienerProcess] - create new Wiener process

	Calling Sequence
	WienerProcess(J) WienerProcess(Sigma)

Parameters

J	-	(optional) stochastic process with non-negative increments, or a deterministic function of time; subordinator
Sigma	-	Matrix; covariance matrix

Description

•	The WienerProcess command creates a new Wiener process. If called with no arguments, the WienerProcess command creates a new standard Wiener process, , that is a Gaussian process with independent increments such that with probability , and for all .

•	The WienerProcess(Sigma) calling sequence creates a Wiener process with covariance matrix Sigma. The matrix Sigma must be a positive semi-definite square matrix. The dimension of the generated process will be equal to the dimension of the matrix Sigma.

•

If an optional parameter J is passed, the WienerProcess command creates a process of the form , where is the standard Wiener process. Note that the subordinator must be an increasing process with non-negative, homogeneous, and independent increments. This can be either another stochastic process such as a Poisson process or a Gamma process, a procedure, or an algebraic expression.

Compatibility

•	The Finance[WienerProcess] command was introduced in Maple 15.

•	For more information on Maple 15 changes, see Updates in Maple 15.

Examples

First create a standard Wiener process and generate replications of the sample path and plot the result.

Define another stochastic variable as an expression involving . You can compute the expected value of using Monte Carlo simulation with the specified number of replications of the sample path.

(1)

(2)

Define another stochastic variable , which also depends on but uses symbolic coefficients. Note that is an Ito process, so it is governed by the stochastic differential equation (SDE) . You can use the Drift and Diffusion commands to compute and .

(3)

(4)

(5)

Create a subordinated Wiener process that uses a Poisson process with intensity parameter as subordinator.

(6)

(7)

Here is a representation of the Ornstein-Uhlenbeck process in terms of or a subordinated Wiener process. In this case the subordinator is a deterministic process that can be specified as a Maple procedure or an algebraic expression.

tau := (exp(2*kappa*t)-1)/(2*kappa)

(8)

(9)

(10)

(11)

	See Also
	Finance[BlackScholesProcess], Finance[CEVProcess], Finance[Diffusion], Finance[Drift], Finance[ExpectedValue], Finance[GeometricBrownianMotion], Finance[ItoProcess], Finance[PathPlot], Finance[SamplePath], Finance[SampleValues], Finance[StochasticProcesses], Finance[WienerProcess]