Optimal Hedging and Pricing of Equity-Linked Life Insurance Contracts in a Discrete-Time Incomplete Market

<table>Optimal risk <svg height="11.7375" id="M507" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 21.225 11.7375" width="21.225" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.7375)">
<g transform="translate(72,-62.61)">
<text transform="matrix(1,0,0,-1,-71.95,62.66)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐌</tspan>
</text>
<text transform="matrix(1,0,0,-1,-60.15,67.83)">
<tspan style="font-size: 8.75px; " x="0" y="0">∗</tspan>
</text>
</g>
</g>
</svg> versus the risk value <svg height="15.85" id="M508" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 14.875 15.85" width="14.875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,15.85)">
<g transform="translate(72,-59.32)">
<g>
<path d="m -71.95,70.71 11.8,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<text transform="matrix(1,0,0,-1,-71.95,59.37)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐌</tspan>
</text>
</g>
</g>
</svg> associated with the optimal return for all cases.</table>

Journal of Probability and Statistics

fig4

Figure 4

Figure 4: Optimal Hedging and Pricing of Equity-Linked Life Insurance Contracts in a Discrete-Time Incomplete Market 