An Approximation of Minimum Initial Capital of Investment Discrete Time Surplus Process with Weibull Distribution in a Reinsurance Company

<table class="fixed-width table-group" id="tab6"><tr><td><table class="table"><colgroup><col style="width:2.50em"/><col style="width:9.04em"/><col style="width:8.42em"/><col style="width:8.42em"/></colgroup><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2"><span style="width: 6.59789ptpx;"><svg height="9.49473pt" id="M227" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.59789 9.49473" width="6.59789pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 111 293 118 346H373Z"></path></g></svg></span></td><td class="align_center">Premium rate </td><td class="align_center">MIC million Baht</td><td class="align_center">MIC million Baht </td></tr><tr class="thead"><td class="align_center"><span style="width: 101.084ptpx;"><svg height="11.7391pt" id="M228" style="vertical-align:-2.45077pt" version="1.1" viewbox="-0.0498162 -9.28833 101.084 11.7391" width="101.084pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M383 397C383 424 344 448 299 448C244 448 172 409 132 375C66 319 23 227 23 146C23 42 74 -12 146 -12C208 -12 298 30 359 103L343 124C315 95 248 48 192 48C145 48 111 85 111 163C111 228 129 294 151 330C171 363 201 401 241 401C275 401 302 384 325 356C332 347 339 344 348 348C373 360 383 381 383 397Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.914,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,20.177,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 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version="1.1" viewbox="-0.0498162 -9.28833 53.2297 11.5564" width="53.2297pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.515,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.778,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,33.018,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,35.982,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,42.222,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z"></path></g><g transform="matrix(.013,0,0,-0.013,48.462,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left">0.1</td><td class="align_center">4.9027</td><td class="align_center">1642.3413</td><td class="align_center">1622.0112</td></tr><tr><td class="align_left">0.2</td><td class="align_center">5.3484</td><td class="align_center">1627.1924</td><td class="align_center">1606.6316</td></tr><tr><td class="align_left">0.3</td><td class="align_center">5.7941</td><td class="align_center">1615.2543</td><td class="align_center">1594.3263</td></tr><tr><td class="align_left">0.4</td><td class="align_center">6.2398</td><td class="align_center">1602.4812</td><td class="align_center">1581.1251</td></tr><tr><td class="align_left">0.5</td><td class="align_center">6.6855</td><td class="align_center">1589.8425</td><td class="align_center">1567.9948</td></tr><tr><td class="align_left">0.6</td><td class="align_center">7.1312</td><td class="align_center">1582.7270</td><td class="align_center">1560.1270</td></tr><tr><td class="align_left">0.7</td><td class="align_center">7.5769</td><td class="align_center">1574.8999</td><td class="align_center">1551.4706</td></tr><tr><td class="align_left">0.8</td><td class="align_center">8.0226</td><td class="align_center">1563.0873</td><td class="align_center">1538.9719</td></tr><tr><td class="align_left">0.9</td><td class="align_center">8.4683</td><td class="align_center">1555.8489</td><td class="align_center">1530.7069</td></tr><tr><td class="align_left">1.0</td><td class="align_center">8.9140</td><td class="align_center">1546.0777</td><td class="align_center">1520.0044</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>The MIC of a reinsurance company has to hold for ensuring that the ruin probability is not greater than <span class="nowrap"><svg height="6.1673pt" id="M226" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 7.51131 6.1673" width="7.51131pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z"></path></g></svg>.</span></div>

Journal of Applied Mathematics

tab6

Table 6

Table 6: An Approximation of Minimum Initial Capital of Investment Discrete Time Surplus Process with Weibull Distribution in a Reinsurance Company 