Use (4.2.21) to derive the following partial differential equation for the floating strike lookback put option Solve

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Use (4.2.21) to derive the following partial differential equation for the floating strike lookback put option 

av  = 0 3 2 ag - (r+) ar 0 < 0, where V (s, t) = Pfe(S, M, t)/S and t = T - t, & = ln . The auxiliary

Solve the above Neumann boundary value problem and check the result with the put price formula given in (4.2.10). 

Define W = ∂V/∂ξ so that W satisfies the same governing differential equation but the boundary condition becomes W(0,τ) = 0. Solve for W(ξ,τ), then integrate W with respect to ξ to obtain V . Be aware that an arbitrary function ∅(t) is generated upon integration with respect to ξ . Obtain an ordinary differential equation for ∅(t) by substituting the solution for V into the original differential equation.

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