以如下为例介绍本书内容：

9 Stochastic Dynamic Programming
With the mathematical background in place, we are ready to study
dynamic programming models that incorporate stochastic shocks. We
study two specifications of the problem. The first of these parallels more
closely the treatment of the deterministic model in Chapter 4, but the
second is more general. The two approaches can be illustrated by two
variations on the one-sector model of optimal growth.
Suppose Lhal the one good. com, can be consumed or used as seed.
Output in any period depends on the quantity of seed planted and on
the quantity of rainfall. Assume that the effect of rainfall is multiplicative.
Rainfall is exogenously determined and stochastic. and may be
serially correlated from year to year. The functional equation for
optimal growth in this economy is
v(k, z) = sup (U[if(k) - y) + (JLv(y, z')Q(z, dr')) .
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In this equation the slate variables are h, the quantity of seed corn
planted in the spring, and z, the quantity of rainfall during the growing
season. The only decision to be made is how much seed com, )'. Lo set
aside for the following year. This decision is made in the fall, given if(k),
the quantity of com han'ested. Since no further uncertaint), intervenes
between fall and spring, y is also the quantit)' planted in the spring.
Alternatively, consider an econom)' in which the quantity of rainfall
does not ftucruate from year to year but in which there are mice in the
storehouse where the seed corn is stored. The size of the mouse population
is exogenously determined and stochastic, and rna)' display serial
correlation from year to year. Assume that the effect of mice is additive.
With rainfall normalized to be unity, the functional equation for optimal