Compound Binomial Model with Batch Markovian Arrival Process

<div>Value of all dividends <span class="nowrap"><svg height="12.7373pt" id="M344" style="vertical-align:-3.429399pt" version="1.1" viewbox="-0.0498162 -9.3079 114.405 12.7373" width="114.405pt" 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="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.384,3.132)"><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,-0.013,15.962,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,27.225,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z"></path></g><g transform="matrix(.013,0,0,-0.013,33.465,0)"><path d="M368 703H309L44 -163H104L368 703Z"></path></g><g transform="matrix(.013,0,0,-0.013,38.826,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z"></path></g><g transform="matrix(.013,0,0,-0.013,47.242,0)"><path d="M433 39L423 65C413 59 399 54 387 54C370 54 352 69 352 114V299C352 352 342 392 307 422C285 440 255 449 225 449C168 437 102 399 75 379C56 365 44 353 44 339C44 315 69 296 87 296C101 296 111 303 116 319C124 349 133 371 145 385C156 397 171 404 190 404C241 404 275 364 275 291V274C253 256 180 229 120 209C65 190 39 159 39 110C39 47 88 -12 159 -12C189 -12 237 25 277 52C282 35 288 21 301 8C312 -3 333 -12 348 -12L433 39ZM275 84C256 65 221 48 195 48C164 48 124 73 124 124C124 161 146 180 185 198C206 208 254 229 275 240V84Z"></path></g><g transform="matrix(.013,0,0,-0.013,52.832,0)"><path d="M524 0V26C466 32 460 36 460 104V297C460 393 411 449 331 449C302 449 276 437 248 419C223 402 201 387 181 372V451C137 432 90 420 42 411V388C96 378 102 374 102 310V104C102 38 97 33 29 26V0H246V26C187 32 181 36 181 104V339C211 365 250 390 290 390C357 390 381 345 381 276V109C381 40 374 32 315 26V0H524Z"></path></g><g transform="matrix(.013,0,0,-0.013,59.89,0)"><path d="M517 51L485 54C448 58 441 63 441 115V712C404 700 337 684 285 678V653C357 648 362 645 362 580V437C339 446 309 449 295 449C159 449 38 340 38 201C38 61 143 -12 223 -12C234 -12 261 -6 301 17L362 53V-12C420 9 495 22 517 26V51ZM362 85C338 67 301 51 266 51C201 51 128 109 128 228C128 373 212 411 259 411C296 411 338 395 362 360V85Z"></path></g><g transform="matrix(.013,0,0,-0.013,69.003,0)"><path d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,76.387,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path></g><g transform="matrix(.013,0,0,-0.013,84.966,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,96.229,0)"><path d="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z"></path></g><g transform="matrix(.013,0,0,-0.013,102.469,0)"><path d="M368 703H309L44 -163H104L368 703Z"></path></g><g transform="matrix(.013,0,0,-0.013,107.83,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z"></path></g></svg>.</span></div>

Mathematical Problems in Engineering

Compound Binomial Model with Batch Markovian Arrival Process

Figure 4