"Cycles" in which the agents solve a different problem in each subperiod

[sbenthall]

(moved from https://github.com/EconForge/dolark/issues/12 )

A feature request: a syntax for writing problems with "cycles" in which the agents solve a different problem in each subperiod.

In these problems:

• All endogenous states are carried from period to period
• All functions (including transition, arbitrage, felicity, etc.) may be different from period to period
• Exogenous shock may vary from period to period.

From @llorracc

A simple example that could be used to develop a syntax for this is the portfolio problem: "end-of-period" problem: Given assets $a$, figure out how to invest them in risky vs safe assets. Which involves constructing a marginal end-of-period-value function $v^{'}{t,1}$ "beginning-of-period" problem: Given end-of-period marginal value function, compute beginning-of-period optimal consumption. This yields $v^{'}{t,0}$

Further technical discussion here: https://www.econ2.jhu.edu/people/ccarroll/SolvingMicroDSOPs/

(originally discussed here: econ-ark/DARKolo#14 (comment) )

[sbenthall]

These kinds of problems are in these lecture notes, section 7 https://llorracc.github.io/SolvingMicroDSOPs/