Approximation for the Finite-Time Ruin Probability of a General Risk Model with Constant Interest Rate and Extended Negatively Dependent Heavy-Tailed Claims

<div class="floats-full-page floats-full-page-other"><h2>Table 1</h2><div class="floats-full-page-caption">Comparison between the analog value and the theoretical result in Theorem <a href="../../852852/#thm2.2">2.2</a>.</div><div class="floats-full-page-content"><table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr /></td></tr><tr class="thead"><td align="left"><span style="width: 56.0625px;"><svg height="16.75" id="M297" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 56.0625 16.75" width="56.0625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.75)">
<g transform="translate(72,-58.6)">
<text transform="matrix(1,0,0,-1,-71.95,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑥</tspan>
<tspan style="font-size: 12.50px; " x="11.040149" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="15.203648" y="0">×</tspan>
<tspan style="font-size: 12.50px; " x="23.205568" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="29.457067" y="0">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-36.24,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">3</tspan>
</text>
<text transform="matrix(1,0,0,-1,-31.36,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">)</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"> Theoretical result</td><td align="center"> Analog value</td></tr><tr><td class="thead-hr" colspan="3"><hr /></td></tr><tr><td align="left">
										0.5
									</td><td align="center"><span style="width: 80.737503px;"><svg height="11.0375" id="M298" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 80.737503 11.0375" width="80.737503" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0375)">
<g transform="translate(72,-63.17)">
<text transform="matrix(1,0,0,-1,-71.95,63.4)">
<tspan style="font-size: 12.50px; " x="0" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="21.880251" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="28.13175" y="0">6</tspan>
<tspan style="font-size: 12.50px; " x="34.383251" y="0">𝑒</tspan>
<tspan style="font-size: 12.50px; " x="42.722752" y="0">−</tspan>
<tspan style="font-size: 12.50px; " x="54.062973" y="0">6</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 135.375px;"><svg height="13.925" id="M299" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 135.375 13.925" width="135.375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.925)">
<g transform="translate(72,-60.86)">
<text transform="matrix(1,0,0,-1,-67.78,63.12)">
<tspan style="font-size: 12.50px; " x="0" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="21.880251" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="28.13175" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="34.383251" y="0">𝑒</tspan>
<tspan style="font-size: 12.50px; " x="42.722752" y="0">−</tspan>
<tspan style="font-size: 12.50px; " x="54.062973" y="0">6</tspan>
<tspan style="font-size: 12.50px; " x="64.477974" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="68.641472" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="74.892967" y="0">6</tspan>
<tspan style="font-size: 12.50px; " x="81.14447" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="84.270218" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="90.521721" y="0">%</tspan>
<tspan style="font-size: 12.50px; " x="99.861458" y="0">)</tspan>
</text>
</g>
</g>
</svg></span></td></tr><tr><td align="left">
										1
									</td><td align="center"><span style="width: 80.737503px;"><svg height="10.9125" id="M300" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 80.737503 10.9125" width="80.737503" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-67.78,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="21.880251" y="0">7</tspan>
<tspan style="font-size: 12.50px; " x="28.13175" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="34.383251" y="0">𝑒</tspan>
<tspan style="font-size: 12.50px; " x="42.722752" y="0">−</tspan>
<tspan style="font-size: 12.50px; " x="54.062973" y="0">7</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 135.375px;"><svg height="13.925" id="M301" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 135.375 13.925" width="135.375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.925)">
<g transform="translate(72,-60.86)">
<text transform="matrix(1,0,0,-1,-67.78,63.12)">
<tspan style="font-size: 12.50px; " x="0" y="0">9</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="21.880251" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="28.13175" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="34.383251" y="0">𝑒</tspan>
<tspan style="font-size: 12.50px; " x="42.722752" y="0">−</tspan>
<tspan style="font-size: 12.50px; " x="54.062973" y="0">7</tspan>
<tspan style="font-size: 12.50px; " x="64.477974" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="68.641472" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="74.892967" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="81.14447" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="84.270218" y="0">7</tspan>
<tspan style="font-size: 12.50px; " x="90.521721" y="0">%</tspan>
<tspan style="font-size: 12.50px; " x="99.861458" y="0">)</tspan>
</text>
</g>
</g>
</svg></span></td></tr><tr><td align="left">
										2
									</td><td align="center"><span style="width: 85.949997px;"><svg height="11.1" id="M302" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 85.949997 11.1" width="85.949997" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1)">
<g transform="translate(72,-63.12)">
<text transform="matrix(1,0,0,-1,-67.78,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="21.880251" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="28.13175" y="0">6</tspan>
<tspan style="font-size: 12.50px; " x="34.383251" y="0">𝑒</tspan>
<tspan style="font-size: 12.50px; " x="42.722752" y="0">−</tspan>
<tspan style="font-size: 12.50px; " x="54.062973" y="0">7</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 127.5625px;"><svg height="13.925" id="M303" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 127.5625 13.925" width="127.5625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.925)">
<g transform="translate(72,-60.86)">
<text transform="matrix(1,0,0,-1,-67.78,63.12)">
<tspan style="font-size: 12.50px; " x="0" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="21.880251" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="28.13175" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="34.383251" y="0">𝑒</tspan>
<tspan style="font-size: 12.50px; " x="42.722752" y="0">−</tspan>
<tspan style="font-size: 12.50px; " x="54.062973" y="0">7</tspan>
<tspan style="font-size: 12.50px; " x="64.477974" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="68.641472" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="74.892967" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="78.018723" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="84.270218" y="0">%</tspan>
<tspan style="font-size: 12.50px; " x="93.609962" y="0">)</tspan>
</text>
</g>
</g>
</svg></span></td></tr><tr><td align="left">
										5
									</td><td align="center"><span style="width: 85.949997px;"><svg height="11.225" id="M304" style="vertical-align:-0.27588pt" version="1.1" viewbox="0 0 85.949997 11.225" width="85.949997" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.225)">
<g transform="translate(72,-63.02)">
<text transform="matrix(1,0,0,-1,-67.78,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">9</tspan>
<tspan style="font-size: 12.50px; " x="21.880251" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="28.13175" y="0">6</tspan>
<tspan style="font-size: 12.50px; " x="34.383251" y="0">𝑒</tspan>
<tspan style="font-size: 12.50px; " x="42.722752" y="0">−</tspan>
<tspan style="font-size: 12.50px; " x="54.062973" y="0">8</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 127.5625px;"><svg height="13.925" id="M305" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 127.5625 13.925" width="127.5625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.925)">
<g transform="translate(72,-60.86)">
<text transform="matrix(1,0,0,-1,-67.78,63.12)">
<tspan style="font-size: 12.50px; " x="0" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="21.880251" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="28.13175" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="34.383251" y="0">𝑒</tspan>
<tspan style="font-size: 12.50px; " x="42.722752" y="0">−</tspan>
<tspan style="font-size: 12.50px; " x="54.062973" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="64.477974" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="68.641472" y="0">6</tspan>
<tspan style="font-size: 12.50px; " x="74.892967" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="78.018723" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="84.270218" y="0">%</tspan>
<tspan style="font-size: 12.50px; " x="93.609962" y="0">)</tspan>
</text>
</g>
</g>
</svg></span></td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr" /></td></tr></table></td></tr></table></div></div>

Table 1 | Approximation for the Finite-Time Ruin Probability of a General Risk Model with Constant Interest Rate and Extended Negatively Dependent Heavy-Tailed Claims

title

Table 1: Approximation for the Finite-Time Ruin Probability of a General Risk Model with Constant Interest Rate and Extended Negatively Dependent Heavy-Tailed Claims

description

Table 1

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