We consider the optimal portfolio problem where the interest rate is stochastic and the agent has insider information on its value at a finite terminal time. The agent's objective is to optimize the terminal value of her portfolio under a logarithmic utility function. Using techniques of initial enlargement of filtration, we identify the optimal strategy and compute the value of the information. The interest rate is first assumed to be an affine diffusion, then more explicit formulas are computed for the Vasicek interest rate model where the interest rate moves according to an Ornstein-Uhlenbeck process. We show that when the interest rate process is correlated with the price process of the risky asset, the value of the information is  infinite, as is usually the case for initial-enlargement-type problems. However since the agent does not know exactly the correlation factor, this may induce an infinite loss instead of an infinite gain. Finally weakening the information own by the agent , and assuming that she only knows a lower-bound  for the terminal value of the interest rate process, we show that the value of the information is finite  .
We consider the optimal portfolio problem where the interest rate is stochastic and the agent has insider information on its value at a finite terminal time. The agent's objective is to optimize the terminal value of her portfolio under a logarithmic utility function. Using techniques of initial enlargement of filtration, we identify the optimal strategy and compute the value of the information. The interest rate is first assumed to be an affine diffusion, then more explicit formulas are computed for the Vasicek interest rate model where the interest rate moves according to an Ornstein-Uhlenbeck process. Incidentally we show that an affine process conditioned to its future value is still an affine process. When the interest rate process is correlated with the price process of the risky asset, the value of the information is proved to be infinite, as is usually the case for initial-enlargement-type problems. However , weakening the information own by the agent and assuming that she only knows a lower-bound or both, a lower and an upper bound, for the terminal value of the interest rate process, we show that the value of the information is finite . This solves by an analytical proof a conjecture stated in Pikovsky and Karatzas (1996) .
R
We show that when
Incidentally we show that an affine process conditioned to its future value is still an affine process. When
A
proved to be
R
since the agent does not know exactly the correlation factor, this may induce an infinite loss instead of an infinite gain. Finally
,
D
,
A
or both, a lower and an upper bound,
A
. This solves by an analytical proof a conjecture stated in Pikovsky and Karatzas (1996)