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5. Consider a non-traded asset whose value is observable at time t given by the dynamics: dX(t) = u(t, x(t)) dt + (t, X(t))dW
5. Consider a non-traded asset whose value is observable at time t given by the dynamics: dX(t) = u(t, x(t)) dt + (t, X(t))dW (t). In addition the market has a bank account dB(t) =rB(t)dt. Consider a fixed T-claim (X(T)). Assume that there exists a pricing function G(t, x) for the claim, satisfying the boundary condition G(T, x) = F(x), and assume that the corresponding volatility function G(t, x) is nonzero.. (a) Show that the market consisting of B and the option I is complete. (b) For any other contingent claim, say (X(T)), obtain the replicating portfolio consisting the assets B and F.
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