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Problems and Solutions in Mathematical Finance: Stochastic Calculus, Volume I by Eric Chin, Sverrir Olafsson, Dian Nel

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5.2 Problems and Solutions

5.2.1 Properties of Poisson Process

  1. 1. Let c05-math-219 be a probability space and let c05-math-220 be a Poisson process with intensity c05-math-221. Show that c05-math-222 and deduce that the correlation coefficient of c05-math-223 and c05-math-224 is
    equation

    Solution

    Since c05-math-225 with c05-math-226, c05-math-227 and by definition

    equation

    For c05-math-228, using the stationary and independent properties ...

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