Precommitted Investment Strategy versus Time-Consistent Investment Strategy for a General Risk Model with Diffusion

<div class="floats-full-page floats-full-page-figure"><h2>Figure 2</h2><div class="floats-full-page-caption"><table>The effect of parameters on optimal precommitted strategy for the C-L risk model.</table></div><div class="floats-full-page-content"><table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="358623.fig.002a" src="https://static-02.hindawi.com/articles/aaa/volume-2014/358623/figures/358623.fig.002a.jpg" /></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>The effect of <svg height="11.9625" id="M261" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 13.6375 11.9625" width="13.6375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M393 379q-9 -16 -28 -29q-15 -10 -23 -2q-19 19 -36 19q-21 0 -52 -38q-57 -72 -82 -126l-40 -197q-23 -3 -75 -18l-7 7q49 196 74 335q7 43 -2 43q-7 0 -30 -14.5t-47 -37.5l-16 23q37 42 82 73t67 31q41 0 15 -113l-11 -50h4q41 71 85 117t77 46q29 0 45 -26&#10;q13 -21 0 -43z" id="x1D45F"></path></g>
<g transform="matrix(.012,-0,0,-.012,7.238,11.762)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105&#10;q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g>
</svg> on optimal precommitted strategy</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="358623.fig.002b" src="https://static-02.hindawi.com/articles/aaa/volume-2014/358623/figures/358623.fig.002b.jpg" /></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>The effect of <svg height="11.825" id="M262" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 13.6375 11.825" width="13.6375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M393 379q-9 -16 -28 -29q-15 -10 -23 -2q-19 19 -36 19q-21 0 -52 -38q-57 -72 -82 -126l-40 -197q-23 -3 -75 -18l-7 7q49 196 74 335q7 43 -2 43q-7 0 -30 -14.5t-47 -37.5l-16 23q37 42 82 73t67 31q41 0 15 -113l-11 -50h4q41 71 85 117t77 46q29 0 45 -26&#10;q13 -21 0 -43z" id="x1D45F"></path></g>
<g transform="matrix(.012,-0,0,-.012,7.238,11.762)"><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> on optimal precommitted strategy</td></tr></table></td></tr><tr class="fig-image" id="c"><td><img alt="358623.fig.002c" src="https://static-02.hindawi.com/articles/aaa/volume-2014/358623/figures/358623.fig.002c.jpg" /></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(c) </b>The effect of <svg height="12.4375" id="M263" style="vertical-align:-0.20064pt" version="1.1" viewbox="0 0 9.5124998 12.4375" width="9.5124998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M529 97q-70 -109 -136 -109q-41 0 -56 94q-23 144 -37 284q-38 -88 -99 -202.5t-93 -156.5q-26 -8 -76 -19l-9 21q71 78 145.5 193t124.5 232q-5 84 -15 128q-12 55 -29.5 75.5t-42.5 20.5q-21 0 -45 -13l-8 24q16 17 46 30t55 13q43 0 70 -46.5t40 -169.5&#10;q27 -249 51 -392q7 -46 23 -46q24 0 70 60z" id="x1D706"></path></g>
</svg> on optimal precommitted strategy</td></tr></table></td></tr><tr class="fig-image" id="d"><td><img alt="358623.fig.002d" src="https://static-02.hindawi.com/articles/aaa/volume-2014/358623/figures/358623.fig.002d.jpg" /></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(d) </b>The effect of <svg height="8.3000002" id="M264" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 9.7250004 8.3000002" width="9.7250004" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,8.038)"><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&#10;q0 -61 24.5 -96.5t65.5 -35.5q51 0 87.5 46.5t50.5 100.5t14 102z" id="x1D70E"></path></g>
</svg> on optimal precommitted strategy</td></tr></table></td></tr><tr class="fig-image" id="e"><td><img alt="358623.fig.002e" src="https://static-02.hindawi.com/articles/aaa/volume-2014/358623/figures/358623.fig.002e.jpg" /></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(e) </b>The effect of <svg height="12.325" id="M265" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 16.0625 12.325" width="16.0625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,8.038)"><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&#10;q0 -61 24.5 -96.5t65.5 -35.5q51 0 87.5 46.5t50.5 100.5t14 102z" id="x1D70E"></path></g>
<g transform="matrix(.012,-0,0,-.012,9.663,12.112)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105&#10;q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g>
</svg> on optimal precommitted strategy</td></tr></table></td></tr><tr class="fig-image" id="f"><td><img alt="358623.fig.002f" src="https://static-02.hindawi.com/articles/aaa/volume-2014/358623/figures/358623.fig.002f.jpg" /></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(f) </b>The effect of <svg height="12.175" id="M266" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 8.6374998 12.175" width="8.6374998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M478 372q0 -39 -31 -97t-61 -98t-78 -98q-45 -55 -73 -102q-13 -79 -13 -197q-11 -11 -43.5 -25.5t-53.5 -15.5l-15 17q5 35 26 101.5t47 123.5q8 72 -1.5 174.5t-37.5 178.5q-14 37 -29 37q-20 0 -67 -65l-25 21q37 60 73 90.5t63 30.5q47 0 72 -112q13 -56 17.5 -141.5&#10;t0.5 -143.5h2q155 193 155 297q0 26 -12 47q-5 8 -5 15q0 16 12.5 27t29.5 11q21 0 34 -21t13 -55z" id="x1D6FE"></path></g>
</svg> on optimal precommitted strategy</td></tr></table></td></tr></table></div></div>

Figure 2 | Precommitted Investment Strategy versus Time-Consistent Investment Strategy for a General Risk Model with Diffusion

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Figure 2: Precommitted Investment Strategy versus Time-Consistent Investment Strategy for a General Risk Model with Diffusion

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Figure 2

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<p><em>Abstract and Applied Analysis</em> publishes research with an emphasis on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimisation theory, and control theory.</p>


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Abstract and Applied Analysis publishes research with an emphasis on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimisation theory, and control theory.