Closed-Form Solutions for Optimal Portfolio Selection with Stochastic Interest Rate and Investment Constraints

30 Pages Posted: 2 Oct 2005

See all articles by Jerome Detemple

Jerome Detemple

Boston University - Department of Finance & Economics; Center for Interuniversity Research and Analysis on Organization (CIRANO)

Marcel Rindisbacher

Questrom School of Business, Boston University; Center for Interuniversity Research and Analysis on Organization (CIRANO)

Abstract

We examine the portfolio choice problem of an investor with constant relative risk aversion in a financial market with partially hedgeable interest rate risk. The individual shadow price of the portfolio constraint is characterized as the solution of a new backward equation involving Malliavin derivatives. A generalization of this equation is studied and solved in explicit form. This result, applied to our financial model, yields closed-form solutions for the shadow price and the optimal portfolio. The effects of parameters such as risk aversion, interest rate volatility, investment horizon, and tightness of the constraint are examined. Applications of our method to a monetary economy with inflation risk and to an international setting with currency risk are also provided.

Suggested Citation

Detemple, Jerome and Rindisbacher, Marcel, Closed-Form Solutions for Optimal Portfolio Selection with Stochastic Interest Rate and Investment Constraints. Mathematical Finance, Vol. 15, No. 4, pp. 539-568, October 2005. Available at SSRN: https://ssrn.com/abstract=792225

Jerome Detemple (Contact Author)

Boston University - Department of Finance & Economics ( email )

595 Commonwealth Avenue
Boston, MA 02215
United States
(617) 353-4297 (Phone)
(617) 353 6667 (Fax)

Center for Interuniversity Research and Analysis on Organization (CIRANO)

2020 rue University, 25th Floor
Montreal, Quebec H3C 3J7
Canada

Marcel Rindisbacher

Questrom School of Business, Boston University ( email )

595 Commonwealth Avenue
Boston, MA MA 02215
United States
617 353 4152 (Phone)
617 353 999 (Fax)

Center for Interuniversity Research and Analysis on Organization (CIRANO) ( email )

2020 rue University, 25th Floor
Montreal, Quebec H3C 3J7
Canada

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