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Financial Mathematics by Roman N. Makarov, Giuseppe Campolieti

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Chapter 5

Single-Period Arrow–Debreu Models

5.1 Specification of the Model

5.1.1 Finite-State Economy. Vector Space of Payoffs. Securities

We now turn to a multinomial generalization of the one-period binomial market model. Although single-period models cannot give a realistic representation of a complex, dynamically changing stock market, we use such models to illustrate many important economic principles. Let us begin with the main assumptions.

  • Any economic activity such as trading and consumption takes place only at two times: the initial time t = 0 and the terminal time t = T.
  • The economic environment at time t = 0 is completely known.
  • At time t = T , the economy can be in one of M different states of the world, denoted by ωj,j = 1, 2 ..., ...

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