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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.

MSC:
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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