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Unformatted text preview: e., xi = qi ). Find the imputed probabilities.
13.10 Optimal investment to fund an expense stream. An organization (such as a municipality) knows
its operating expenses over the next T periods, denoted E1 , . . . , ET . (Normally these are positive;
but we can have negative Et , which corresponds to income.) These expenses will be funded by a
combination of investment income, from a mixture of bonds purchased at t = 0, and a cash account.
The bonds generate investment income, denoted I1 , . . . , IT . The cash balance is denoted B0 , . . . , BT ,
where B0 ≥ 0 is the amount of the initial deposit into the cash account. We can have Bt < 0 for
t = 1, . . . , T , which represents borrowing.
After paying for the expenses using investment income and cash, in period t, we are left with
Bt − Et + It in cash. If this amount is positive, it earns interest at the rate r+ > 0; if it is negative,
we must pay interest at rate r− , where r− ≥ r+ . Thus the expenses, investment income, and cash
balances are linked as follows:
Bt+1 = (1 + r+ )(Bt − Et + It ) Bt − Et + It ≥ 0
(1 + r− )(Bt...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.
 Fall '13
 F.Borrelli
 The Aeneid

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