Mean-Variance-CvaR Model of Multiportfolio Optimization via Linear Weighted Sum 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">
								Alt.</td><td align="center" colspan="3">Criteria</td></tr><tr class="thead"><td align="center"><svg height="15.5375" id="M108" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 18.4375 15.5375" width="18.4375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,12.05,15.475)"><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>
</svg>  <br/>0.10</td><td align="center"><svg height="15.5375" id="M109" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 18.4375 15.5375" width="18.4375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.4)"><path d="M682 629q-1 -16 -1.5 -72t-2.5 -86l-31 -4q-5 92 -51 129t-139 37q-100 0 -177 -49t-116 -125t-39 -162q0 -122 66 -201t182 -79q83 0 137 42.5t112 128.5l26 -15q-12 -31 -42.5 -88t-45.5 -75q-139 -27 -199 -27q-148 0 -243 81.5t-95 226.5q0 173 129.5 274.5
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<g transform="matrix(.012,-0,0,-.012,12.05,15.475)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg>  <br/>0.05</td><td align="center"><svg height="15.6875" id="M110" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 18.4375 15.6875" width="18.4375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.4)"><path d="M682 629q-1 -16 -1.5 -72t-2.5 -86l-31 -4q-5 92 -51 129t-139 37q-100 0 -177 -49t-116 -125t-39 -162q0 -122 66 -201t182 -79q83 0 137 42.5t112 128.5l26 -15q-12 -31 -42.5 -88t-45.5 -75q-139 -27 -199 -27q-148 0 -243 81.5t-95 226.5q0 173 129.5 274.5
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<g transform="matrix(.012,-0,0,-.012,12.05,15.475)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
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</svg>  <br/>0.30</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td align="left"><span style="width: 18.975px;"><svg height="15.9375" id="M111" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 18.975 15.9375" width="18.975" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.788)"><path d="M689 25v-25h-322v25l32 3q46 4 46 33q0 31 -46 136h-225l-13 -34q-31 -78 -31 -97q0 -36 81 -41v-25h-202v25q36 6 53 28q18 22 46 92l221 545h28l222 -522q36 -87 58 -117q21 -26 52 -26zM189 236h195l-101 243z" id="x1D400"></path></g>
<g transform="matrix(.012,-0,0,-.012,12.337,15.875)"><path d="M441 24v-24h-373v24q75 2 96 20q22 19 22 85v378q0 70 -36 70q-26 0 -65 -16l-20 -8v26l251 109h18v-570q0 -57 19 -75q19 -17 88 -19z" id="x1D7CF"></path></g>
</svg></span></td><td align="center">15</td><td align="center">10</td><td align="center">25</td></tr><tr><td align="left"><span style="width: 18.975px;"><svg height="15.9375" id="M112" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 18.975 15.9375" width="18.975" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.788)"><path d="M689 25v-25h-322v25l32 3q46 4 46 33q0 31 -46 136h-225l-13 -34q-31 -78 -31 -97q0 -36 81 -41v-25h-202v25q36 6 53 28q18 22 46 92l221 545h28l222 -522q36 -87 58 -117q21 -26 52 -26zM189 236h195l-101 243z" id="x1D400"></path></g>
<g transform="matrix(.012,-0,0,-.012,12.337,15.875)"><path d="M453 211h25l-46 -211h-415v23q97 102 151 166q42 49 81 110q51 78 51 148q0 56 -31.5 91.5t-87.5 35.5q-77 0 -122 -90h-28q67 204 223 204q82 0 132 -49.5t50 -133.5q0 -110 -114 -218l-162 -154h140q82 0 107 13q27 13 46 65z" id="x1D7D0"></path></g>
</svg></span></td><td align="center">30</td><td align="center">20</td><td align="center">10</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: Mean-Variance-CvaR Model of Multiportfolio Optimization via Linear Weighted Sum Method 