### Abstract

An agent can invest in a high‐yield bond and a low‐yield bond, holding either long or short positions in either asset. Any movement of money between these two assets incurs a transaction cost proportional to the size of the transaction. the low‐yield bond is liquid in the sense that wealth invested in this bond can be consumed directly without a transaction cost; wealth invested in the high‐yield bond can be consumed only by first moving it into the low‐yield bond. the problem of optimal consumption and investment on an infinite planning horizon is solved for a class of utility functions larger than the class of power functions.

Original language | English (US) |
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Pages (from-to) | 53-84 |

Number of pages | 32 |

Journal | Mathematical Finance |

Volume | 1 |

Issue number | 3 |

DOIs | |

State | Published - Jul 1991 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Accounting
- Finance
- Social Sciences (miscellaneous)
- Economics and Econometrics
- Applied Mathematics

### Keywords

- free boundary
- optimal control
- transaction costs
- utility maximization
- variational inequality

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## Cite this

Shreve, S. E., Soner, H. M., & Xu, G. L. (1991). Optimal Investment and Consumption With Two Bonds and Transaction Costs.

*Mathematical Finance*,*1*(3), 53-84. https://doi.org/10.1111/j.1467-9965.1991.tb00016.x