[732] | 1 | #LyX 1.6.4 created this file. For more info see http://www.lyx.org/ |
---|
| 2 | \lyxformat 345 |
---|
| 3 | \begin_document |
---|
| 4 | \begin_header |
---|
| 5 | \textclass scrartcl |
---|
| 6 | \options DIV=12 |
---|
| 7 | \use_default_options true |
---|
| 8 | \language english |
---|
| 9 | \inputencoding auto |
---|
| 10 | \font_roman ae |
---|
| 11 | \font_sans default |
---|
| 12 | \font_typewriter default |
---|
| 13 | \font_default_family default |
---|
| 14 | \font_sc false |
---|
| 15 | \font_osf false |
---|
| 16 | \font_sf_scale 100 |
---|
| 17 | \font_tt_scale 100 |
---|
| 18 | |
---|
| 19 | \graphics default |
---|
| 20 | \paperfontsize default |
---|
| 21 | \spacing single |
---|
| 22 | \use_hyperref false |
---|
| 23 | \papersize default |
---|
| 24 | \use_geometry false |
---|
| 25 | \use_amsmath 1 |
---|
| 26 | \use_esint 1 |
---|
| 27 | \cite_engine basic |
---|
| 28 | \use_bibtopic false |
---|
| 29 | \paperorientation portrait |
---|
| 30 | \secnumdepth 3 |
---|
| 31 | \tocdepth 3 |
---|
| 32 | \paragraph_separation indent |
---|
| 33 | \defskip medskip |
---|
| 34 | \quotes_language english |
---|
| 35 | \papercolumns 1 |
---|
| 36 | \papersides 1 |
---|
| 37 | \paperpagestyle default |
---|
| 38 | \tracking_changes false |
---|
| 39 | \output_changes false |
---|
| 40 | \author "" |
---|
| 41 | \author "" |
---|
| 42 | \end_header |
---|
| 43 | |
---|
| 44 | \begin_body |
---|
| 45 | |
---|
| 46 | \begin_layout Title |
---|
| 47 | System pro simulaci |
---|
| 48 | \end_layout |
---|
| 49 | |
---|
| 50 | \begin_layout Section* |
---|
| 51 | Puvodni zadani: |
---|
| 52 | \end_layout |
---|
| 53 | |
---|
| 54 | \begin_layout Standard |
---|
| 55 | Vychazime ze zadani |
---|
| 56 | \begin_inset CommandInset citation |
---|
| 57 | LatexCommand cite |
---|
| 58 | key "ThoClu:05" |
---|
| 59 | |
---|
| 60 | \end_inset |
---|
| 61 | |
---|
| 62 | : |
---|
| 63 | \end_layout |
---|
| 64 | |
---|
| 65 | \begin_layout Standard |
---|
| 66 | \begin_inset Formula \begin{eqnarray} |
---|
| 67 | SYSTEM:\,\, y_{t+1} & = & y_{t}+bu_{t}+\sigma e_{t},\,\,\, e_{t}\sim\mathcal{N}(0,1),\label{eq:sys}\\ |
---|
| 68 | ZTRATA:\,\,\,\,\, L_{t} & = & (y_{t+1}-r_{t+1})^{2}\nonumber \end{eqnarray} |
---|
| 69 | |
---|
| 70 | \end_inset |
---|
| 71 | |
---|
| 72 | Reseni schematicky: |
---|
| 73 | \end_layout |
---|
| 74 | |
---|
| 75 | \begin_layout Standard |
---|
| 76 | \begin_inset Formula \begin{equation} |
---|
| 77 | V_{t}=\min_{u_{t}}\mathsf{E}_{e_{t},b}\left\{ L_{t}+V_{t+1}|y_{t},u_{t-1},y_{t-1},u_{t-2},\ldots\right\} \label{eq:dp}\end{equation} |
---|
| 78 | |
---|
| 79 | \end_inset |
---|
| 80 | |
---|
| 81 | kde stredni hodnota se pocita pres neurcitost v |
---|
| 82 | \begin_inset Formula $e_{t}$ |
---|
| 83 | \end_inset |
---|
| 84 | |
---|
| 85 | a pres neurcitost v |
---|
| 86 | \begin_inset Formula $b$ |
---|
| 87 | \end_inset |
---|
| 88 | |
---|
| 89 | . |
---|
| 90 | \end_layout |
---|
| 91 | |
---|
| 92 | \begin_layout Standard |
---|
| 93 | Pro linearni a Gausovsky system ( |
---|
| 94 | \begin_inset CommandInset ref |
---|
| 95 | LatexCommand ref |
---|
| 96 | reference "eq:sys" |
---|
| 97 | |
---|
| 98 | \end_inset |
---|
| 99 | |
---|
| 100 | ) je k dispozici konjugovana hustota ve forme Normalniho rozlozeni pravdepodobno |
---|
| 101 | sti |
---|
| 102 | \begin_inset Formula $f(b_{t})=\mathcal{N}(\hat{b}_{t},P_{t}),$ |
---|
| 103 | \end_inset |
---|
| 104 | |
---|
| 105 | jejiz parametry se vyvijeji rekurzivne, rovnice (28) v |
---|
| 106 | \begin_inset CommandInset citation |
---|
| 107 | LatexCommand cite |
---|
| 108 | key "ThoClu:05" |
---|
| 109 | |
---|
| 110 | \end_inset |
---|
| 111 | |
---|
| 112 | . |
---|
| 113 | Tim padem je mozne vycislit ocekavanou hodnotu pres |
---|
| 114 | \begin_inset Formula $b$ |
---|
| 115 | \end_inset |
---|
| 116 | |
---|
| 117 | v ( |
---|
| 118 | \begin_inset CommandInset ref |
---|
| 119 | LatexCommand ref |
---|
| 120 | reference "eq:dp" |
---|
| 121 | |
---|
| 122 | \end_inset |
---|
| 123 | |
---|
| 124 | ) analyticky: |
---|
| 125 | \begin_inset Formula \begin{eqnarray*} |
---|
| 126 | V_{t} & = & \min_{u_{t}}\mathsf{E}_{e_{t},b}\left\{ (y_{t}+bu_{t}+\sigma e_{t}-r_{t+1})^{2}+V_{t+1}|y_{t},u_{t-1},y_{t-1},u_{t-2},\ldots\right\} \\ |
---|
| 127 | & = & \min_{u_{t}}\mathsf{E}_{e_{t}}\left\{ (y_{t}+\hat{b}u_{t}+\sigma e_{t}-r_{t+1})^{2}+P_{t}u_{t}^{2}|y_{t},u_{t-1},y_{t-1},u_{t-2},\ldots\right\} +\\ |
---|
| 128 | & & +\mathsf{E}_{e_{t},b}\left\{ V_{t+1}|y_{t},u_{t-1},y_{t-1},u_{t-2},\ldots\right\} \end{eqnarray*} |
---|
| 129 | |
---|
| 130 | \end_inset |
---|
| 131 | |
---|
| 132 | Muzeme provest preznaceni |
---|
| 133 | \begin_inset Formula \[ |
---|
| 134 | V_{t+1}(H_{t})=\mathsf{E}_{e_{t},b}\left\{ V_{t+1}|y_{t},u_{t-1},y_{t-1},u_{t-2},\ldots\right\} \] |
---|
| 135 | |
---|
| 136 | \end_inset |
---|
| 137 | |
---|
| 138 | kde |
---|
| 139 | \begin_inset Formula $H_{t}=[y_{t},\hat{b}_{t},P_{t}]$ |
---|
| 140 | \end_inset |
---|
| 141 | |
---|
| 142 | . |
---|
| 143 | Vysledna uloha je ekvivalentni tomu, kdyby zadani bylo: |
---|
| 144 | \end_layout |
---|
| 145 | |
---|
| 146 | \begin_layout Standard |
---|
| 147 | \begin_inset Formula \begin{eqnarray*} |
---|
| 148 | SYSTEM:\,\, H_{t+1} & = & \left[\begin{array}{c} |
---|
| 149 | y_{t+1}\\ |
---|
| 150 | \hat{b}_{t+1}\\ |
---|
| 151 | P_{t+1}\end{array}\right]=\left[\begin{array}{c} |
---|
| 152 | y_{t}+\hat{b}_{t}u_{t}\\ |
---|
| 153 | (28)\\ |
---|
| 154 | (28)\end{array}\right]+\left[\begin{array}{c} |
---|
| 155 | \sigma e_{t}\\ |
---|
| 156 | 0\\ |
---|
| 157 | 0\end{array}\right]\\ |
---|
| 158 | ZTRATA:\,\,\,\,\, L_{t} & = & (y_{t+1}-r_{t+1})^{2}+P_{t}u_{t}^{2}.\end{eqnarray*} |
---|
| 159 | |
---|
| 160 | \end_inset |
---|
| 161 | |
---|
| 162 | |
---|
| 163 | \end_layout |
---|
| 164 | |
---|
| 165 | \begin_layout Standard |
---|
| 166 | (28) je opet rovnice (28) z |
---|
| 167 | \begin_inset CommandInset citation |
---|
| 168 | LatexCommand cite |
---|
| 169 | key "ThoClu:05" |
---|
| 170 | |
---|
| 171 | \end_inset |
---|
| 172 | |
---|
| 173 | . |
---|
| 174 | Takto upravenou ulohu muzeme resit pomoci algoritmu |
---|
| 175 | \begin_inset CommandInset citation |
---|
| 176 | LatexCommand cite |
---|
| 177 | key "TodTas:09" |
---|
| 178 | |
---|
| 179 | \end_inset |
---|
| 180 | |
---|
| 181 | . |
---|
| 182 | \begin_inset CommandInset citation |
---|
| 183 | LatexCommand cite |
---|
| 184 | key "Ber:01" |
---|
| 185 | |
---|
| 186 | \end_inset |
---|
| 187 | |
---|
| 188 | |
---|
| 189 | \begin_inset CommandInset bibtex |
---|
| 190 | LatexCommand bibtex |
---|
| 191 | bibfiles "vs-world,world_classics,mk,world" |
---|
| 192 | options "plain" |
---|
| 193 | |
---|
| 194 | \end_inset |
---|
| 195 | |
---|
| 196 | |
---|
| 197 | \end_layout |
---|
| 198 | |
---|
| 199 | \end_body |
---|
| 200 | \end_document |
---|