The attacks on the World Trade Center in New York, the subway and bus bombings in London, and the suicide bombings in Casablanca are only a few of the examples in which in recent years, terrorists have opted to attack multiple targets at once. Often, their strong determination to attack makes it impossible to completely deter terrorists from attacking altogether, and instead, counterterrorist units must consider how to defend targets effectively to minimize damages. We attempt to model a version of this scenario by presenting a two target sequential game where two players try to attack and defend the targets respectively. The probability of successfully destroying a target is a function of resource allocations from both players, who are also subject to budget constraints. We attempt to find the defender’s strategy that will minimize expected damages by first exploring the attacker’s optimal strategy. We show that the attacker’s decision to attack only one or both targets is dependent on the size of the attacker’s allowed budget relative to other game parameters, and use that information to evaluate the defender’s strategy. We also numerically determine the optimal defender security investment, as well its sensitivity to other game parameters. We conjecture that as the damage and expected reward at a target increases, the defender’s allocation towards that target tends to increase, while an increase in the punishment results in the opposite effect. Such conjectures allow for the creation of a flexible defense policy in the more applicable bigger picture.

Submitted by Jean Medeiros (jeanletras@uepb.edu.br) on 2016-04-19T14:22:53Z No. of bitstreams: 1 PDF - Wilson Luiz dos Santos Filho.pdf: 775879 bytes, checksum: 770072135e50de9b9e1f8f021d84d6e2 (MD5) / Approved for entry into archive by Secta BC (secta.csu.bc@uepb.edu.br) on 2016-07-22T20:25:20Z (GMT) No. of bitstreams: 1 PDF - Wilson Luiz dos Santos Filho.pdf: 775879 bytes, checksum: 770072135e50de9b9e1f8f021d84d6e2 (MD5) / Made available in DSpace on 2016-07-22T20:25:32Z (GMT). No. of bitstreams: 1 PDF - Wilson Luiz dos Santos Filho.pdf: 775879 bytes, checksum: 770072135e50de9b9e1f8f021d84d6e2 (MD5) Previous issue date: 2014-11-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / From the analysis of Financial Mathematics teaching in Brazil and the confirmation that the majority of the Brazilian population deals, in an inefficient way, with financial tran- sactions, we proposed in this work a strategy to approach a kind of Financial Mathematics capable of turning this theme much more meaningful to High School Students. We recal- led the basic concepts of Financial Mathematics, went through the Financial Education in Brazil, discussed the main Amortization Systems practiced in our country with day-by-day examples and, finally, we presented an interesting application in the calculation of car loans, describing the characteristics of Leasing and Personal Credit (CDC). Besides that, we eli- cited the calculations of Total Effective Cost (CET) of a transaction, applying the use of a Financial Calculator. / A partir da análise acerca do ensino da Matemática Financeira no Brasil e da consta- tação de que grande parte do povo brasileiro lida de forma ineficiente com transações finan- ceiras, propusemos neste trabalho, uma estratégia de abordagem da Matemática Financeira capaz de tornar mais significativo aos alunos do Ensino Médio este tema. Recordamos os conceitos básicos daMatemática Financeira, passeamos pela Educação Financeira no Brasil, discutimos os principais Sistemas de Amortização praticados em nosso país com exemplos corriqueiros e, finalmente, apresentamos uma aplicação interessante no cálculo de um finan- ciamento de veículo, descrevendo as características Leasing e CDC, além de evidenciarmos o cálculo do Custo Efetivo Total (CET) de uma transação, recorrendo ao uso de uma Calcu- ladora Financeira.