Asymptotic Behavior of Tail Density for Sum of Correlated Lognormal Variables

<table>Left tail <svg height="17.262501" id="M144" style="vertical-align:-4.0404pt" version="1.1" viewbox="0 0 24.112499 17.262501" width="24.112499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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t-82 -49t-49 -148l-24 -127q42 -36 88 -36q79 0 126 61.5t47 157.5z" id="x1D70C"></path></g><g transform="matrix(.017,-0,0,-.017,13.933,12.012)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,28.637,12.012)"><path d="M548 455q-32 -77 -74 -77q-37 0 -103 10l-3 -2q36 -30 48.5 -62t12.5 -80q0 -103 -75 -179.5t-175 -76.5q-70 0 -113 45t-43 128q0 115 83.5 200.5t209.5 85.5q31 0 77.5 -4t67.5 -4q36 0 62 30zM350 274q0 54 -17 86q-19 35 -57 35q-50 0 -90 -37.5t-59 -91.5t-19 -109
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<g transform="matrix(.012,-0,0,-.012,38.25,16.087)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
<g transform="matrix(.017,-0,0,-.017,44.588,12.012)"><path d="M368 703l-264 -866h-60l265 866h59z" id="x2F"></path></g><g transform="matrix(.017,-0,0,-.017,51.591,12.012)"><path d="M548 455q-32 -77 -74 -77q-37 0 -103 10l-3 -2q36 -30 48.5 -62t12.5 -80q0 -103 -75 -179.5t-175 -76.5q-70 0 -113 45t-43 128q0 115 83.5 200.5t209.5 85.5q31 0 77.5 -4t67.5 -4q36 0 62 30zM350 274q0 54 -17 86q-19 35 -57 35q-50 0 -90 -37.5t-59 -91.5t-19 -109
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</svg>. g_2 is the approximation.</table>

International Journal of Mathematics and Mathematical Sciences

fig2

Figure 2

Figure 2: Asymptotic Behavior of Tail Density for Sum of Correlated Lognormal Variables 