Optimal Investment and Consumption With Two Bonds and Transaction Costs

S. E. Shreve, H. M. Soner, G. ‐L Xu

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


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 languageEnglish (US)
Pages (from-to)53-84
Number of pages32
JournalMathematical Finance
Issue number3
StatePublished - Jul 1991
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


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


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