### Inspiring Video

If you want to understand more about why one serious quantitative researcher is interested in this approach, we recommend [Lars Peter Hansen's Nobel lecture](http://www.nobelprize.org/mediaplayer/index.php?id=1994).

If you want to understand more about why one serious quantitative researcher is interested in this approach, we recommend [Lars Peter Hansen's Nobel lecture](https://www.nobelprize.org/prizes/economic-sciences/2013/hansen/lecture/).

### Other References

To fit in with [our earlier lecture on LQ control](https://python-intro.quantecon.org/lqcontrol.html), we will treat loss minimization rather than value maximization.

To begin, recall the [infinite horizon LQ problem](https://python-intro.quantecon.org/lqcontrol.html#Infinite-Horizon), where an agent chooses a sequence of controls $\{u_t\}$ to minimize

To begin, recall the [infinite horizon LQ problem](https://python.quantecon.org/lqcontrol.html#infinite-horizon), where an agent chooses a sequence of controls $\{u_t\}$ to minimize

```{math}

:label: rob_sih

$$

The operator $\mathcal B$ is the standard (i.e., non-robust) LQ Bellman operator, and $P = \mathcal B(P)$ is the standard matrix Riccati equation coming from the

Bellman equation --- see [this discussion](https://python-intro.quantecon.org/lqcontrol.html#Infinite-Horizon).

Bellman equation --- see [this discussion](https://python.quantecon.org/lqcontrol.html#infinite-horizon).

Under some regularity conditions (see {cite}`HansenSargent2008`), the operator $\mathcal B \circ \mathcal D$

has a unique positive definite fixed point, which we denote below by $\hat P$.

What's striking about this optimization problem is that it is once again an LQ discounted dynamic programming problem, with $\mathbf w = \{ w_t \}$ as the sequence of controls.

The expression for the optimal policy can be found by applying the usual LQ formula ([see here](https://python-intro.quantecon.org/lqcontrol.html#Infinite-Horizon)).

The expression for the optimal policy can be found by applying the usual LQ formula ([see here](https://python.quantecon.org/lqcontrol.html#infinite-horizon)).

We denote it by $K(F, \theta)$, with the interpretation $w_{t+1} = K(F, \theta) x_t$.

x_{t+1} = (A + C K) x_t + B u_t

```

Once again, the expression for the optimal policy can be found [here](https://python-intro.quantecon.org/lqcontrol.html#Infinite-Horizon) --- we denote

Once again, the expression for the optimal policy can be found [here](https://python.quantecon.org/lqcontrol.html#infinite-horizon) --- we denote

it by $\tilde F$.

(rb_eq)=

\beta (A - B \hat F)' \tilde P (A - B \hat F)

```

(revisit [this discussion](https://python-intro.quantecon.org/lqcontrol.html#Infinite-Horizon) if you don't know where {eq}`rb_a2be` comes from) and the optimal policy is

(revisit [this discussion](https://python.quantecon.org/lqcontrol.html#infinite-horizon) if you don't know where {eq}`rb_a2be` comes from) and the optimal policy is

$$

w_{t+1} = - \beta (\beta \theta I + \beta C' \tilde P C)^{-1}