Optimal portfolios with anticipating information on the stochastic interest rate

TL;DR

This paper develops a mathematical framework to incorporate anticipatory information about future interest rate trends into optimal portfolio strategies, using affine diffusion models and filtration enlargement techniques.

Contribution

It introduces explicit formulas for utility gains from future interest rate information, extending to Markov chain-based models with jumps and parameter modulation.

Findings

Explicit formulas for utility improvement with anticipatory info

Extension to Markov chain models with jumps

Numerical analysis illustrating theoretical results

Abstract

By employing the technique of enlargement of filtrations, we demonstrate how to incorporate information about the future trend of the stochastic interest rate process into a financial model. By modeling the interest rate as an affine diffusion process, we obtain explicit formulas for the additional expected logarithmic utility in solving the optimal portfolio problem. We begin by solving the problem when the additional information directly refers to the interest rate process, and then extend the analysis to the case where the information relates to the values of an underlying Markov chain. The dynamics of this chain may depend on anticipated market information, jump at predefined epochs, and modulate the parameters of the stochastic interest rate process. The theoretical study is then complemented by an illustrative numerical analysis.