Worst-Case Investment and Reinsurance Optimization for an Insurer under Model Uncertainty

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/ddns/volume-2016/9693419/figures/9693419.fig.002a.svgz" name="9693419.fig.002a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Effect of <svg height="9.25202pt" id="M219" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 9.96544 9.25202" width="9.96544pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M393 379C402 394 400 411 393 422C384 437 365 448 348 448C301 448 237 372 186 285H182L193 335C210 408 205 448 178 448C150 448 80 402 29 344L45 321C80 355 114 373 122 373C128 373 130 365 124 330C106 228 76 98 50 -5L57 -12C82 -5 112 3 132 6L172 203C196 256 234 304 254 329C275 355 293 367 306 367C318 367 330 360 342 348C347 343 355 343 365 350S386 367 393 379Z" id="g113-115"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="422" vert-adv-y="422"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,4.901,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg> on reinsurance strategy</td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/ddns/volume-2016/9693419/figures/9693419.fig.002b.svgz" name="9693419.fig.002b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>Effect of <svg height="9.14241pt" id="M220" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -5.96091 9.96544 9.14241" width="9.96544pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M393 379C402 394 400 411 393 422C384 437 365 448 348 448C301 448 237 372 186 285H182L193 335C210 408 205 448 178 448C150 448 80 402 29 344L45 321C80 355 114 373 122 373C128 373 130 365 124 330C106 228 76 98 50 -5L57 -12C82 -5 112 3 132 6L172 203C196 256 234 304 254 329C275 355 293 367 306 367C318 367 330 360 342 348C347 343 355 343 365 350S386 367 393 379Z" id="g113-115"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="422" vert-adv-y="422"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,4.901,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg> on reinsurance strategy</td></tr><tr class="fig-image" id="c"><td><object data="https://static.hindawi.com/articles/ddns/volume-2016/9693419/figures/9693419.fig.002c.svgz" name="9693419.fig.002c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b>Effect of <svg height="9.4347pt" id="M221" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -6.14359 11.8314 9.4347" width="11.8314pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M548 455L523 469C505 448 490 439 461 439C416 439 374 447 316 447C144 447 23 310 23 161C23 47 89 -12 179 -12C312 -12 429 106 429 244C429 303 419 344 368 386L371 388C404 383 440 378 474 378C507 378 530 411 548 455ZM350 274C350 191 308 25 198 25C144 25 108 75 108 157C108 264 170 395 276 395C296 395 320 384 333 360C347 334 350 316 350 274Z" id="g113-240"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="565" vert-adv-y="565"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.76,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg> on reinsurance strategy</td></tr><tr class="fig-image" id="d"><td><object data="https://static.hindawi.com/articles/ddns/volume-2016/9693419/figures/9693419.fig.002d.svgz" name="9693419.fig.002d" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(d) </b>Effect of <svg height="9.32509pt" id="M222" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -6.14359 11.8314 9.32509" width="11.8314pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M548 455L523 469C505 448 490 439 461 439C416 439 374 447 316 447C144 447 23 310 23 161C23 47 89 -12 179 -12C312 -12 429 106 429 244C429 303 419 344 368 386L371 388C404 383 440 378 474 378C507 378 530 411 548 455ZM350 274C350 191 308 25 198 25C144 25 108 75 108 157C108 264 170 395 276 395C296 395 320 384 333 360C347 334 350 316 350 274Z" id="g113-240"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="565" vert-adv-y="565"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.76,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg> on reinsurance strategy</td></tr></table>

<div>The effect of parameters on optimal reinsurance strategy.</div>

Discrete Dynamics in Nature and Society

fig2

Figure 2

Figure 2: Worst-Case Investment and Reinsurance Optimization for an Insurer under Model Uncertainty 