Adv. Math. Econ. 8, 231-255 (2006)

Solving long term optimal investment problems with Cox-Ingersoll-Ross interest rates

Hiroaki Hata^{1} and Jun Sekine^{2}

1 Graduate School of Engineering Sience,Osaka University,Toyonaka,Osaka 560-8531,Japan

2 Institut of Economic Researsh,Kyoto University,Yoshida-Honmachi,Sakyo-ku,Kyoto 606-801 Japan

Received: April 27, 2005 Revised: September 27, 2005

JEL classification: C61, G11

Mathematical Subject Classification (2000): 49L20, 60F10, 91B28

Abstract. A large deviations control problem is treated for a long term optimal investment on a financial market with a bank account and a risky stock, both of which are affected by a stochastic factor described as Cox-Ingersoll-Ross’s interest rates. The solution is presented in explicit form by investigating the effective domain of the associated risk-sensitive control problem in risk-seeking case.

Key words: large deviations control, risk-sensitive control, long-term investment, power utility, CIR-interest rates