Pricing Participating Products under a Generalized Jump-Diffusion Model

<table>Probabilities that the terminal asset
value <svg height="13.45" id="M475" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 30.3375 13.45" width="30.3375" xmlns="http://www.w3.org/2000/svg">
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<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐴</tspan>
<tspan style="font-size: 12.50px; " x="8.9646511" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="13.12815" y="0">𝑇</tspan>
<tspan style="font-size: 12.50px; " x="20.004801" y="0">)</tspan>
</text>
</g>
</g>
</svg> is less than the terminal policy reserve <svg height="13.45" id="M476" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 30.700001 13.45" width="30.700001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑅</tspan>
<tspan style="font-size: 12.50px; " x="9.2522202" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="13.415719" y="0">𝑇</tspan>
<tspan style="font-size: 12.50px; " x="20.29237" y="0">)</tspan>
</text>
</g>
</g>
</svg> under <svg height="11.1" id="M477" style="vertical-align:-0.1881pt" version="1.1" viewbox="0 0 14.35 11.1" width="14.35" 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,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝒫</tspan>
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</g>
</svg>.</table>

International Journal of Stochastic Analysis

fig9

Figure 9

Figure 9: Pricing Participating Products under a Generalized Jump-Diffusion Model 