Editor:
Universidad Carlos III de Madrid. Departamento de Estadística

Issued date:
2017-11-01

ISSN:
2387-0303

Sponsor:
The first author acknowledge financial support from the Spanish Ministry of
Education and Science, research projects MTM2015– 72907–EXP and MTM2013–42104–P (via FEDER funds).

Serie/No.:
UC3M Working papers. Statistics and Econometrics 17-17

Project:
Gobierno de España. MTM2015-72907-EXP Gobierno de España. MTM2013-42104-P

Keywords:
Optimal portfolio
,
Enlargement of filtrations
,
Vasicek interest rate model
,
Value of the information

Rights:
Atribución-NoComercial-SinDerivadas 3.0 España

Abstract:

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 herportfolio under a logarithmic utility fuWe 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 herportfolio 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.[+][-]