Question: Kindly help solve this question. (i) State the martingale representation theorem, including conditions for its application, defining all terms used. [3] Let 5, denote the

Kindly help solve this question. (i) State the martingale representation theorem, including conditions for its application, defining all terms used. [3] Let 5,

Kindly help solve this question.

denote the price of an underlying security at time r; / denotes

the risk free rate of return expressed in continuously compounded form, B,

(i) State the martingale representation theorem, including conditions for its application, defining all terms used. [3] Let 5, denote the price of an underlying security at time r; / denotes the risk free rate of return expressed in continuously compounded form, B, represents an accumulated "bank account" at time ( that earns the risk free rate of return. Let X be any derivative payment contingent on Fr, payable at some fixed future time T. where Fris the sigma algebra generated by S,, for O S u S T. You may assume that, under the equivalent measure O, the process D, = er'S, is a martingale and that dS, = BrD, it + dD,) (ii) Show that the value of this derivative at time /

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