[J(u) = x(T)]
The optimal solution is to invest $10,000 in Option A at time 0, yielding a maximum return of $14,400 at time 1. Dynamic Programming And Optimal Control Solution Manual
| (t) | (x) | (y) | (V(t, x, y)) | | --- | --- | --- | --- | | 0 | 10,000 | 0 | 12,000 | | 0 | 0 | 10,000 | 11,500 | | 1 | 10,000 | 0 | 14,400 | | 1 | 0 | 10,000 | 13,225 | [J(u) = x(T)] The optimal solution is to
[\dotx(t) = (A - BR^-1B'P)x(t)]
[\dotx(t) = v(t)] [\dotv(t) = u(t) - g]
Solving this equation using dynamic programming, we obtain: yielding a maximum return of $14
[V(t, x, y) = \max_x', y' R_A(x') + R_B(y') + V(t+1, x', y')]