The CASHMGMT.ltx Model

Cash Balance Management

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In this example, suppose you are managing a cash account for which each day there is a random input or output of cash. If the cash level gets too high, we want to transfer some of the cash to a longer term investment account that pays a higher interest rate, whereas if the cash account gets too low, we want to transfer funds from a longer term account into the cash account, so that we always have sufficient cash on hand. Because we require discrete scenarios, the cash on hand status is represented as multiples of $1000. In order to avoid negative subscripts, the following correspondence between cash on hand and state must be made:

Cash of hand:-2000-1000010002000300040005000
Only three transitions are possible: go down one state, stay put, or go up one state. Their probabilities are:
PDN=.4; PUT=.1; PUP=.5
However, for state one, the probability of going down one state is zero. Likewise, for state eight, the probability of going up one state is zero. So, their probabilities are:
For one PDN=0; PUT=.5; PUP=.5;
For eight PDN=.4; PUT=.6; PUP=0.
We can make any state change we want, but there is a fixed cost f making any change:
and a variable cost proportional to the amount of change:


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