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authorKarl Berry <karl@freefriends.org>2010-11-04 00:10:45 +0000
committerKarl Berry <karl@freefriends.org>2010-11-04 00:10:45 +0000
commitd84ed04dce1fca7ecbdbc8a503e9a7106f950058 (patch)
tree5d85cdfcad69b8cc2e16e7954e3b0c9d7d245642 /Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex
parent802438b15253966cad1d595d71fb05e5ff7441aa (diff)
pst-func 0.71 (3nov10)
git-svn-id: svn://tug.org/texlive/trunk@20299 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex')
-rw-r--r--Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex29
1 files changed, 16 insertions, 13 deletions
diff --git a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex
index 5051ed450c5..10b31b92ba3 100644
--- a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex
+++ b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex
@@ -1,4 +1,4 @@
-%% $Id: pst-func-doc.tex 391 2010-10-02 16:43:32Z herbert $
+%% $Id: pst-func-doc.tex 411 2010-11-03 07:58:25Z herbert $
\documentclass[11pt,english,BCOR10mm,DIV12,bibliography=totoc,parskip=false,
smallheadings, headexclude,footexclude,oneside]{pst-doc}
\usepackage[utf8]{inputenc}
@@ -61,6 +61,7 @@ Rafal Bartczuk,
Buddy Ledger,
Manuel Luque,
Patrice Mégret,
+ Matthias Rüss,
Jose-Emilio Vila-Forcen,
Timothy Van Zandt,
Michael Zedler,
@@ -1473,21 +1474,23 @@ starts \Lcs{psWeinbull} with 0.
\clearpage
\subsection{Vasicek distribution}
-The model specifies that the instantaneous interest rate follows the stochastic differential equation:
+For a homogenous portfolio of infinite granularity the portfolio loss
+distribution is given by
-\begin{align}
-\mathrm{d}r_t = a(b-r_t)\, \mathrm{d}t + \sigma \, \mathrm{d}W_t
-\end{align}
-with the solution:
+\[
+\mathbb{P}(L(P)<x)=1-\mathcal{N}
+ \left(\frac{\mathcal{N}^{-1}(PD)-\sqrt{1-R2}\cdot\mathcal{N}^{-1}(x)}{R}
+ \right)
+\]
+$L(P)$ denotes the portfolio loss in percent. $pd$ is the uniform default
+probability and $R2$ is the uniform asset correlation.
+
+They are preset to $pd=0.22$ and $R2=0.11$ and can be overwritten in the
+usual way. The macro uses the PostScript function norminv from the package
+pst-math
+which is loaded by default and also shown in the following example.
-\begin{align}
- r(t) = r(0) e^{-a t} + b \left(1- e^{-a t}\right) + \sigma e^{-a t}\int_0^t e^{a s}\,dW_s
-\end{align}
-Possible parameters are \Lkeyword{pd} for the probability of the defualt portfolio
-and \Lkeyword{R2}, the R$_\mathrm{squared}$ of the portfolio. They are preset to 0.22 and 0.11
-and can be overwritten in the usual way. The macro uses the PostScript function \Lps{norminv}
-from the package \LPack{pst-math} which is loaded by default and also shown in the following example.
\begin{LTXexample}[pos=t]
\psset{xunit=5}