Mathematical Finance

Q.2 Given the function V (t, z)
lim V( t, z ) / (t, z) = ∞ is said to
is said to be decreasing in convex and in z if and only if V < 1.
Q.3 V(t,x,y) = dXt = rXt dt + t(µ-r) + tdWt – Ct dt + Yt dtdXt = rXt dt + t(µ-r) + tdWt – Ct dt + Yt dt = stochastic differential equation
let f(t, x, y) = logeXft = 0, fx = 1/x, fxx = -1/x2
df = 0 dt + ½ dx – 1/2x * 1/2 (dx)2
= 1/x (dXt = rXt dt + t(µ-r) + tdWt – Ct dt + Yt dt) – 1/2x * ½ (2×2 dt)
HJB = V( x,t,y) / t = ½ ydW2t + [V( x, t, y) / x]rXt –[t(µ-r)]2 (V(x, t, y)/ x) + 2/2 * 2V(x, t, y) / x2