14.8. EXERCISES 261 EXERCISE 14.4 (Abstract to Concrete Portfolio Weights). In general, the port- folio weights (Qc, be) of martingale pricing theory are given by the familiar formulas uw,t) u(w, t) (14.85) Q = and be = U. - dw, t) dw,t) D. On the other hand, the PDE method can be applied under the classic Black-Scholes model with constant , o, and r to show that for the call option with strike price K the replicating portfolio has the concrete weights (14.86) felt, St) + TB. where f(t, x) is given by the Black-Scholes formula (14.24). Show that the concrete weights (14.86) may be obtained from the more abstract weights by exploiting the fact that we have two representations for the arbitrage price of the call option: Fit, S.) = B. Eg((ST-K)+/Br|Fi) = BU. 14.8. EXERCISES 261 EXERCISE 14.4 (Abstract to Concrete Portfolio Weights). In general, the port- folio weights (Qc, be) of martingale pricing theory are given by the familiar formulas uw,t) u(w, t) (14.85) Q = and be = U. - dw, t) dw,t) D. On the other hand, the PDE method can be applied under the classic Black-Scholes model with constant , o, and r to show that for the call option with strike price K the replicating portfolio has the concrete weights (14.86) felt, St) + TB. where f(t, x) is given by the Black-Scholes formula (14.24). Show that the concrete weights (14.86) may be obtained from the more abstract weights by exploiting the fact that we have two representations for the arbitrage price of the call option: Fit, S.) = B. Eg((ST-K)+/Br|Fi) = BU