0

Bellman equation:

$V(x) = max \{F(x,y)+ \beta V(y)\}$

$V(x) = max \{F(x,y), \beta V(y)\}$

When to use the plus and when to use the comma?

Do they get the same form of sequence problem?

Would you mind give me an example to explain such difference?

Thank you very much !

XJ.C
  • 245
  • What are the ranges of $x$ and $y$? – marty cohen Jun 15 '16 at 04:38
  • x , y $\in \mathbb{R}$@martycohen – XJ.C Jun 15 '16 at 04:47
  • It seems that the difference should not depends on the ranges of x and y@martycohen – XJ.C Jun 15 '16 at 05:38
  • The first one should by maximized over to x and y. The second one choose the greater one of $F(x,y)$ and $\beta V(y)$. But you should ask for the whole Bellman equation and not posting an uncomplete expression. – callculus42 Jun 15 '16 at 05:54
  • The first one can be written as a sequence problem: $V(x_0) = max \sum \beta^t F(x_t,x_{t+1}) $. Does the second one get the same sequence problem?@callculus – XJ.C Jun 15 '16 at 06:09

0 Answers0