Analysis of Relativity Premium in Bonus-Malus System Based on Optimal Linear Method

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td align="left" rowspan="2">Staring level</td><td align="center" colspan="3">Level  occupied  if</td></tr><tr class="thead"><td align="center"><span style="width: 29.0065ptpx;"><svg height="8.91176pt" id="M92" style="vertical-align:-0.2130003pt" version="1.1" viewbox="-0.0498162 -8.69876 29.0065 8.91176" width="29.0065pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z" id="g113-111"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="502" vert-adv-y="502"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,10.586,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,22.324,0)"><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" id="g113-49"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg></span></td><td align="center"><span style="width: 29.0065ptpx;"><svg height="8.91176pt" id="M93" style="vertical-align:-0.2130003pt" version="1.1" viewbox="-0.0498162 -8.69876 29.0065 8.91176" width="29.0065pt" xmlns="http://www.w3.org/2000/svg" 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550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg></span></td><td align="center"><span style="width: 29.0065ptpx;"><svg height="11.3596pt" id="M94" style="vertical-align:-2.23926pt" version="1.1" viewbox="-0.0498162 -9.12034 29.0065 11.3596" width="29.0065pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z" id="g113-111"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="502" vert-adv-y="502"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,10.586,0)"><path d="M531 359V409L57 624V568L473 384L57 201V145L531 359ZM531 34V84H57V34H531ZM531 -114V-64H57V-114H531Z" id="g114-71"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,22.324,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z" id="g113-51"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg></span></td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td align="left">1</td><td align="center">1</td><td align="center">3</td><td align="center">6</td></tr><tr><td align="left">2</td><td align="center">1</td><td align="center">4</td><td align="center">6</td></tr><tr><td align="left">3</td><td align="center">2</td><td align="center">5</td><td align="center">6</td></tr><tr><td align="left">4</td><td align="center">3</td><td align="center">6</td><td align="center">6</td></tr><tr><td align="left">5</td><td align="center">4</td><td align="center">6</td><td align="center">6</td></tr><tr><td align="left">6</td><td align="center">5</td><td align="center">6</td><td align="center">6</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab1

Table 1

Table 1: Analysis of Relativity Premium in Bonus-Malus System Based on Optimal Linear Method 