Role of index bonds in an optimal dynamic asset allocation model with real subsistence consumption

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Original languageEnglish
Pages (from-to)710-731
Journal / PublicationApplied Mathematics and Computation
Issue number1
Publication statusPublished - 1 Mar 2006
Externally publishedYes


We investigate the role of index bonds in a dynamic consumption and asset allocation model where the rate of real consumption at any given time cannot fall below a fixed level. An explicit form of the optimal consumption and portfolio rule for a class of Constant Relative Risk Aversion (CRRA) utility functions is derived. Consumption increases above the subsistence level only when wealth exceeds a threshold value. Risky investments in equity and nominal bonds are initially proportional to the excess of wealth over a lower bound, and then increase nonlinearly with wealth. The desirability of investing in the risky assets are related to the agent's risk preference, the equity premium, and the inflation risk premium. The demand for index bonds is also obtained. The results should be useful for the management of defined benefit pension funds, university endowments, and other portfolios which have a withdrawal pre-commitment in real terms. © 2005 Elsevier Inc. All rights reserved.

Research Area(s)

  • Bellman equation, Index bonds, Inflation risk, Portfolio choice, Portfolio insurance