Appl Math Optim (2011) 64:217–255
Insider Models with Finite Utility in Markets
Arturo Kohatsu-Higa · Makoto Yamazato
Published online: 21 April 2011
© Springer Science+Business Media, LLC 2011
Abstract In this article we consider, under a Lévy process model for the stock price,
the utility optimization problem for an insider agent whose additional information
is the ﬁnal price of the stock blurred with an additional independent noise which
vanishes as the ﬁnal time approaches. Our main interest is establishing conditions
under which the utility of the insider is ﬁnite. Mathematically, the problem entails the
study of a “progressive” enlargement of ﬁltration with respect to random measures.
We study the jump structure of the process which leads to the conclusion that in most
cases the utility of the insider is ﬁnite and his optimal portfolio is bounded. This can
be explained ﬁnancially by the high risks involved in models with jumps.
Keywords Asymmetric markets · Markets driven by Lévy processes · Enlargement
The problem of asymmetric markets in continuous time mathematical ﬁnance has
been considered since Karatzas-Pikovski . They dealt with a ﬁnancial market
where the underlying follows a geometric Brownian motion model. An insider is an
The authors acknowledge ﬁnancial support from grants of the Japanese government and thank the
referee for various comments that lead to improvements in the presentation.
A. Kohatsu-Higa (
Department of Mathematical Sciences, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga,
Department of Mathematics, Faculty of Science, University of the Ryukyus, Senbaru 1,
Nishihara-cho, Okinawa, 903-0213, Japan