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A theory of bond portfolios. (English) Zbl 1125.91051
Summary: We introduce a bond portfolio management theory based on foundations similar to those of stock portfolio management. A general continuous-time zero-coupon market is considered. The problem of optimal portfolios of zero-coupon bonds is solved for general utility functions, under a condition of no-arbitrage in the zero-coupon market. A mutual fund theorem is proved, in the case of deterministic volatilities. Explicit expressions are given for the optimal solutions for several utility functions.

91B28 Finance etc. (MSC2000)
49J55 Existence of optimal solutions to problems involving randomness
60H07 Stochastic calculus of variations and the Malliavin calculus
90C46 Optimality conditions and duality in mathematical programming
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