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Optimal consumption/portfolio choice with borrowing rate higher than deposit rate

Published online by Cambridge University Press:  17 February 2009

Wensheng Xu  and
Shuping Chen
Wensheng Xu
Affiliation:
Department of Applied Mathematics, Zhejiang University, Hangzhou, 310027, P. R. China.
Shuping Chen
Affiliation:
Department of Applied Mathematics, Zhejiang University, Hangzhou, 310027, P. R. China.
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Abstract

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In this paper, optimal consumption and investment decisions are studied for an investor who has available a bank account and a stock whose price is a log normal diffusion. The bank pays at an interest rate r(t) for any deposit, and vice takes at a larger rate r′(t) for any loan. Optimal strategies are obtained via Hamilton-Jacobi-Bellman (HJB) equation which is derived from dynamic programming principle. For the specific HARA case, we get the optimal consumption and optimal investment explicitly, which coincides with the classical one under the condition r′(t) ≡ r(t)

Type
Research Article
Information
The ANZIAM Journal , Volume 39 , Issue 4 , April 1998 , pp. 449 - 462
Copyright
Copyright © Australian Mathematical Society 1998

References

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