Role of Index Bonds in an Optimal Dynamic Asset Allocation Model with Real Subsistence Consumption

Applied Mathematics and Computation, Vol. 174, No. 1, pp. 710-731, 2006

25 Pages Posted: 4 Apr 2006

See all articles by Ning Gong

Ning Gong

Deakin University; Financial Research Network (FIRN)

Tao Li

City University of Hong Kong (CityUHK) - Department of Economics & Finance

Abstract

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.

Keywords: Portfolio choice, Portfolio insurance, Index bonds, Bellman equation, Inflation risk

JEL Classification: G12

Suggested Citation

Gong, Ning and Li, Tao, Role of Index Bonds in an Optimal Dynamic Asset Allocation Model with Real Subsistence Consumption. Applied Mathematics and Computation, Vol. 174, No. 1, pp. 710-731, 2006. Available at SSRN: https://ssrn.com/abstract=894400

Ning Gong

Deakin University ( email )

Department of Finance
Faculty of Business and Law
Burwood, Victoria 3125
Australia
+61 3 9246 8492 (Phone)

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

Tao Li (Contact Author)

City University of Hong Kong (CityUHK) - Department of Economics & Finance ( email )

83 Tat Chee Avenue
Kowloon
Hong Kong

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