bv_cvxbook_extra_exercises

# we will assume that the index weights c rn as well

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Unformatted text preview: − Et + It ) Bt − Et + It &lt; 0, for t = 1, . . . , T − 1. We take B1 = (1 + r+ )B0 , and we require that BT − ET + IT = 0, which means the ﬁnal cash balance, plus income, exactly covers the ﬁnal expense. The initial investment will be a mixture of bonds, labeled 1, . . . , n. Bond i has a price Pi &gt; 0, a coupon payment Ci &gt; 0, and a maturity Mi ∈ {1, . . . , T }. Bond i generates an income stream 110 given by (i) at = Ci t &lt; Mi C i + 1 t = Mi 0 t &gt; Mi , for t = 1, . . . , T . If xi is the number of units of bond i purchased (at t = 0), the total investment cash ﬂow is (1) (n ) It = x1 at + · · · + xn at , t = 1, . . . , T. We will require xi ≥ 0. (The xi can be fractional; they do not need to be integers.) The total initial investment required to purchase the bonds, and fund the initial cash balance at t = 0, is x1 P1 + · · · + xn Pn + B0 . (a) Explain how to choose x and B0 to minimize the total initial investment required to fund the expense stream. (b) Solve the problem instance given...
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