CHAPTER 9
Optimal Investment with
Inflation-Linked Products
Taras Beletski and Ralf Korn∗
9.1 INTRODUCTION
With the growing number of traded inflation linked bonds and inflation
linked life insurance products there is also a growing interest in models
for the evolution of inflation indexes and the inclusion of inflation linked
financial products into an optimal portfolio of an investor who is otherwise
investing in bonds and stocks. We will look at this problem in a model
that is a combination of the standard diffusion type model of continuous-
time portfolio optimization and a modeling framework for inflation indexes
described in Korn and Kruse (2004) (which itself is in some aspects related
to Jarrow and Yildirim, 2003).
There, an inflation index such as the harmonized consumer price index
(HCPI) is modelled as a (generalized) geometric Brownian motion with a
drift equal to the difference of the nominal and the real interest rate. This
modeling process will be shortly described in section 9.2. As a consequence
of it there will be Black–Scholes type formulae for the prices of inflation
linked bonds and options on inflation. Picking up an approach of Korn and
Trautmann (1999) – later generalized by Kraft (2003) – a mixed investment
problem including those products and conventional investment into stocks
∗The work of Taras Beletski was supported by the DFG-Graduiertenkolleg “Mathematik und
Praxis”. The work of Ralf Korn was supported by the Rheinland-Pfalz excellence cluster
“Dependable adaptive systems and mathematical modeling”.
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