Optimal Consumption and Investment Strategies with Stochastic Interest Rates

44 Pages Posted: 10 May 2001

See all articles by Claus Munk

Claus Munk

Copenhagen Business School

Carsten Sørensen

Copenhagen Business School - Department of Finance

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Date Written: February 2001

Abstract

We characterize the solution to the consumption and investment problem of a time-additive power utility investor in a continuous-time dynamically complete market with stochastic changes in the opportunity set. It is demonstrated that under stochastic interest rates the investor optimally hedges against changes in the term structure of interest rates by investing in a coupon bond, or portfolio of bonds, with a payment schedule that matches the forward-expected (i.e. certainty equivalent) consumption pattern. This is of conceptual importance since the hedge portfolio only depends on the specic term structure dynamics through the consequences for the optimal consumption pattern. We consider two explicit examples where the term structure dynamics are given by the Vasicek model and a three factor non-Markovian Heath-Jarrow-Morton model.

Suggested Citation

Munk, Claus and Sørensen, Carsten, Optimal Consumption and Investment Strategies with Stochastic Interest Rates (February 2001). EFA 2001 Barcelona Meetings; EFMA 2001 Lugano Meetings. Available at SSRN: https://ssrn.com/abstract=269475 or http://dx.doi.org/10.2139/ssrn.269475

Claus Munk

Copenhagen Business School ( email )

Department of Finance
Solbjerg Plads 3
Frederiksberg, DK-2000
Denmark

HOME PAGE: http://sites.google.com/view/clausmunk/home

Carsten Sørensen (Contact Author)

Copenhagen Business School - Department of Finance ( email )

Solbjerg Plads 3
Frederiksberg, DK-2000
Denmark

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