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CLOSED‐FORM SOLUTIONS FOR OPTIMAL PORTFOLIO SELECTION WITH STOCHASTIC INTEREST RATE AND INVESTMENT CONSTRAINTS
Author(s) -
Detemple Jér^me,
Rindisbacher Marcel
Publication year - 2005
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2005.00250.x
Subject(s) - economics , interest rate , portfolio , econometrics , constraint (computer aided design) , risk free interest rate , risk aversion (psychology) , portfolio optimization , financial economics , mathematics , expected utility hypothesis , monetary economics , geometry
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.