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Fixed colours.

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Stéphane Adjemian (Hermes) 2016-06-21 00:07:21 +02:00
parent f7a5f36068
commit 2f9adec224
1 changed files with 13 additions and 13 deletions
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slides/ep.tex
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@ -25,7 +25,7 @@
\begin{document}
\title{The stochastic extended path approach}
\author{St\'ephane Adjemian\footnote{Universit\'e du Maine} and Michel Juillard\footnote{Banque de France}}
\date{April, 2016}
\date{June, 2016}
\begin{frame}
\titlepage{}
@ -155,10 +155,10 @@ linenodelimiter=.
\begin{split}
s_t &= \mathsf Q({\color{red}s_{t-1}},{\color{gray}u_t})\\
0 &= \mathsf F \bigl({\color{blue}y_t},{\color{red}x_t},s_t,\mathscr E (y_{t+1},x_{t+1},s_{t},0)\bigr)\\
0 &= \mathsf G (y_t,{\color{blue}x_{t+1}},{\color{red}x_t},s_t)\\
0 &= \mathsf G ({\color{blue}y_t},{\color{blue}x_{t+1}},{\color{red}x_t},s_t)\\
s_{t+1} &= \mathsf Q(s_{t},0)\\
0 &= \mathsf F \bigl(y_{t+1},x_{t+1},s_{t+1},\mathscr E (y_{t+2},x_{t+2},s_{t+1},0)\bigr)\\
0 &= \mathsf G (y_{t+1},x_{t+2},x_{t+1},s_{t+1})\\
0 &= \mathsf F \bigl(y_{t+1},{\color{blue}x_{t+1}},s_{t+1},\mathscr E (y_{t+2},x_{t+2},s_{t+1},0)\bigr)\\
0 &= \mathsf G (y_{t+1},x_{t+2},{\color{blue}x_{t+1}},s_{t+1})\\
&\vdots\\
s_{t+h} &= \mathsf Q(s_{t+h-1},0)\\
0 &= \mathsf F \bigl(y_{t+h},x_{t+h},s_{t+h},\mathscr E (y_{t+h+1},x_{t+h+1},s_{t+h},0)\bigr)\\
@ -382,10 +382,10 @@ For $i=1,\dots,m$
\begin{split}
s_t &= \mathsf Q({\color{red}s_{t-1}},{\color{gray}u_t})\\
0 &= \mathsf F \left({\color{blue}y_t},{\color{red}x_t},s_t,{\sum} _i \omega_i \mathscr E (y_{t+1}^i,x_{t+1},s_{t},\mathfrc u_i)\right)\\
0 &= \mathsf G (y_t,{\color{blue}x_{t+1}},{\color{red}x_t},s_t)\\
0 &= \mathsf G ({\color{blue}y_t},{\color{blue}x_{t+1}},{\color{red}x_t},s_t)\\
s_{t+1}^i &= \mathsf Q(s_{t},\mathfrc u_i)\\
0 &= \mathsf F \bigl(y_{t+1}^i,x_{t+1},s_{t+1}^i,\mathscr E (y_{t+2}^i,x_{t+2}^i,s_{t+1}^i,0)\bigr)\\
0 &= \mathsf G (y_{t+1}^i,x_{t+2}^i,x_{t+1},s_{t+1}^i)\\
0 &= \mathsf F \bigl(y_{t+1}^i,{\color{blue}x_{t+1}},s_{t+1}^i,\mathscr E (y_{t+2}^i,x_{t+2}^i,s_{t+1}^i,0)\bigr)\\
0 &= \mathsf G (y_{t+1}^i,x_{t+2}^i,{\color{blue}x_{t+1}},s_{t+1}^i)\\
&\vdots\\
s_{t+h}^i &= \mathsf Q(s_{t+h-1}^i,0)\\
0 &= \mathsf F \bigl(y_{t+h}^i,x_{t+h}^i,s_{t+h}^i,\mathscr E (y_{t+h+1}^i,x_{t+h+1}^i,s_{t+h}^i,0)\bigr)\\
@ -405,10 +405,10 @@ For all $(i,j)\in \left\{1,\dots,m\right\}^2$
\begin{split}
s_t &= \mathsf Q({\color{red}s_{t-1}},{\color{gray}u_t})\\
0 &= \mathsf F \left({\color{blue}y_t},{\color{red}x_t},s_t,{\sum} _i \omega_i \mathscr E (y_{t+1}^i,x_{t+1},s_{t},\mathfrc u_i)\right)\\
0 &= \mathsf G (y_t,{\color{blue}x_{t+1}},{\color{red}x_t},s_t)\\
0 &= \mathsf G ({\color{blue}y_t},{\color{blue}x_{t+1}},{\color{red}x_t},s_t)\\
s_{t+1}^i &= \mathsf Q(s_{t},\mathfrc u_i)\\
0 &= \mathsf F \bigl(y_{t+1}^i,x_{t+1},s_{t+1}^i,{\sum} _j \omega_j \mathscr E (y_{t+2}^{i,j},x_{t+2}^i,s_{t+1}^i,\mathfrc u_j)\bigr)\\
0 &= \mathsf G (y_{t+1}^i,x_{t+2}^i,x_{t+1},s_{t+1}^i)\\
0 &= \mathsf F \bigl(y_{t+1}^i,{\color{blue}x_{t+1}},s_{t+1}^i,{\sum} _j \omega_j \mathscr E (y_{t+2}^{i,j},x_{t+2}^i,s_{t+1}^i,\mathfrc u_j)\bigr)\\
0 &= \mathsf G (y_{t+1}^i,x_{t+2}^i,{\color{blue}x_{t+1}},s_{t+1}^i)\\
s_{t+2}^{i,j} &= \mathsf Q(s_{t+1}^i,\mathfrc u_j)\\
&\vdots\\
s_{t+h}^{i,j} &= \mathsf Q(s_{t+h-1}^{i,j},0)\\
@ -648,10 +648,10 @@ capture the effect of future volatility?
\begin{split}
s_t &= \mathsf Q({\color{red}s_{t-1}},{\color{gray}u_t})\\
0 &= \mathsf F \left({\color{blue}y_t},{\color{red}x_t},s_t,{\sum} _i \omega_i \mathscr E \left(y_{t+1}^i+\frac{1}{2}g_{\sigma\sigma},x_{t+1},s_{t},\mathfrc u_i\right)\right)\\
0 &= \mathsf G (y_t,{\color{blue}x_{t+1}},{\color{red}x_t},s_t)\\
0 &= \mathsf G ({\color{blue}y_t},{\color{blue}x_{t+1}},{\color{red}x_t},s_t)\\
s_{t+1}^i &= \mathsf Q(s_{t},\mathfrc u_i)\\
0 &= \mathsf F \bigl(y_{t+1}^i,x_{t+1},s_{t+1}^i,\mathscr E (y_{t+2}^i,x_{t+2}^i,s_{t+1}^i,0)\bigr)\\
0 &= \mathsf G (y_{t+1}^i,x_{t+2}^i,x_{t+1},s_{t+1}^i)\\
0 &= \mathsf F \bigl(y_{t+1}^i,{\color{blue}x_{t+1}},s_{t+1}^i,\mathscr E (y_{t+2}^i,x_{t+2}^i,s_{t+1}^i,0)\bigr)\\
0 &= \mathsf G (y_{t+1}^i,x_{t+2}^i,{\color{blue}x_{t+1}},s_{t+1}^i)\\
&\vdots\\
s_{t+h}^i &= \mathsf Q(s_{t+h-1}^i,0)\\
0 &= \mathsf F \bigl(y_{t+h}^i,x_{t+h}^i,s_{t+h}^i,\mathscr E (y_{t+h+1}^i,x_{t+h+1}^i,s_{t+h}^i,0)\bigr)\\