Kernel-Based Aggregating Learning System for Online Portfolio Optimization

<div>Diagram of the KAL system. It is a detailed demonstration of (<a href="https://static-preview.hindawi.com/articles/mpe/volume-2020/6595329/figures/#EEq21">21</a>): <svg height="15.6446pt" id="M184" style="vertical-align:-4.0532pt" version="1.1" viewbox="-0.0498162 -11.5914 62.9998 15.6446" width="62.9998pt" 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="M41 650V615C111 608 121 602 121 516V134C121 48 111 42 32 35V0H289C413 0 518 27 592 83C668 141 717 229 717 351C717 446 678 517 628 564C564 625 467 650 341 650H41ZM255 540C255 569 257 586 265 595C272 602 292 609 328 609C397 609 450 589 491 547C537 502 566 426 566 331C566 152 474 43 340 43C270 43 255 68 255 140V540Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.893,3.132)"><path d="M329 433H203L239 587L230 596L147 534L123 433H57L30 395L34 388H115L61 129C37 16 59 -12 85 -12C147 -12 222 58 260 98L241 125C212 95 160 62 144 62C132 62 127 71 138 126L192 386L305 394L329 433Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.051,3.132)"><path d="M556 236V289H337V504H275V289H56V236H275V-4H337V236H556Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.611,3.132)"><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"></path></g><g transform="matrix(.013,0,0,-0.013,27.222,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,38.485,0)"><path d="M699 0V35C659 41 632 57 591 109C519 200 445 301 381 397C426 443 468 491 527 545C582 597 623 609 685 615V650H425V615L443 613C490 607 492 592 468 561C435 516 395 467 328 399C298 368 273 352 252 346V516C252 602 260 608 331 615V650H37V615C112 608 121 602 121 516V134C121 48 111 42 39 35V0H338V35C261 42 252 48 252 134V314C267 316 280 310 301 280C372 176 455 59 498 0H699Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,47.624,-5.741)"><path d="M556 236V289H56V236H556Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,53.184,-5.741)"><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"></path></g><g transform="matrix(.0091,0,0,-0.0091,47.624,3.784)"><path d="M485 418C485 434 469 451 441 451C389 451 312 387 255 335C221 304 194 278 159 242H157L259 678C264 698 264 710 255 710C242 710 183 681 96 673L90 643L128 642C165 641 171 640 162 602L24 -5L31 -12C51 -4 81 4 110 9L145 181C154 195 180 220 205 242C233 170 263 106 291 53C318 1 335 -12 360 -12C383 -12 425 0 483 82L463 105C437 79 411 57 400 57C388 57 378 68 355 110C329 156 288 244 268 298C299 333 355 376 405 376C426 376 440 373 448 368C453 365 465 368 468 373C477 386 485 405 485 418Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,52.256,3.784)"><path d="M556 236V289H337V504H275V289H56V236H275V-4H337V236H556Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,57.816,3.784)"><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"></path></g></svg> calculated by (<a href="https://static-preview.hindawi.com/articles/mpe/volume-2020/6595329/figures/#EEq18">18</a>) is exploited to adjust the tracking strength and optimization influence of different assets. Then, it increases investment in assets with the positive sign in normalized price relative prediction and decreases investment in the negative ones. <svg height="15.9773pt" id="M185" style="vertical-align:-3.4007pt" version="1.1" viewbox="-0.0498162 -12.5766 21.5866 15.9773" width="21.5866pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,.339,-3.549)"><path d="M470 557C393 591 314 624 246 666H224C156 624 76 591 0 557L12 532C86 550 163 573 235 596C309 572 384 550 458 532L470 557Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.761,3.132)"><path d="M329 433H203L239 587L230 596L147 534L123 433H57L30 395L34 388H115L61 129C37 16 59 -12 85 -12C147 -12 222 58 260 98L241 125C212 95 160 62 144 62C132 62 127 71 138 126L192 386L305 394L329 433Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.919,3.132)"><path d="M556 236V289H337V504H275V289H56V236H275V-4H337V236H556Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,16.479,3.132)"><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"></path></g></svg> controls the step size.</div>

Mathematical Problems in Engineering

fig3

Figure 3

Figure 3: Kernel-Based Aggregating Learning System for Online Portfolio Optimization 