# Solving Stochastic Dynamic Optimization Problems: A difficulty with Lagrange Multipliers

In Wickens' Macroeconomics book, in page 552, the author states the following:

«The stochastic problem can be solved using the method of Lagrange multipliers, but there is a problem with this solution.»

However, if I'm not mistaken, it's very usual to see other books using lagrange multipliers to solve this type of problems. Are they wrong? Am I wrong? Is there a way to go around this apparent limitation?

Any help would be appreciated.

Here's a the image:

Following a comment exchange below another answer, the critical detail of a link offered by the OP as an example of by-passing/ignoring Wicken's comment/argument, and one different from Wickens' formulation, is that in the link's eq. $(4)$,
$$\lambda_t = \beta E_t[\lambda_{t+1}(1+r_t)]$$
the multiplier $\lambda_{t+1}$ appears together with the interest rate of period $t$, which is assumed part of the information set at $t$ and so not a random variable in the specific equation. So the authors can proceed in the 2nd line after eq. $(6)$ to write the marginal rate of substitution as they do, without the need to assume uncorrelatedness between the multiplier/marginal utility of consumption, and the interest rate.
This goes back to how they formulate the income resource constraint (page 2 middle), where it is essentially assumed that the household has, at the beginning of period $t$, available assets or debt $(1+r_{t-1})B_t$. The authors explicitly discuss this "timing convention" immediately after eq. $(1)$
"Note a timing convention -$r_{t-1}$ is the interest you have to pay today on existing debt. $r_t$ is what you will have to pay tomorrow, but you choose how much debt to take into tomorrow today. Hence, we assume that households observe $r_t$ in time $t$. Hence we can treat $r_t$ as known from the perspective of time $t$."