Question: Consider a stock whose price per share is modeled by using the standard geometric Brownian motion model dS(t) = rS(t)dt + S(t)dW(t), where W(t) is

Consider a stock whose price per share is modeled by using the standard geometric Brownian motion model

dS(t) = rS(t)dt + S(t)dW(t),

where W(t) is a standard Brownian motion under the risk-neutral probability measure, r > 0 is the interest rate and > 0 is the volatility. Consider now a contingent claim on the underlying stock with maturity date T and payoff

V (T) = aS(T) + b, where a, b are two positive real numbers.

Compute in closed-form the arbitrage free price, v(t,s), of this claim at time t, for the current value of the stock s.

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