Appl Math Optim (2009) 60: 275–296
Portfolio Optimization in a Semi-Markov Modulated
Mrinal K. Ghosh · Anindya Goswami ·
Suresh K. Kumar
Published online: 21 April 2009
© Springer Science+Business Media, LLC 2009
Abstract We address a portfolio optimization problem in a semi-Markov modulated
market. We study both the terminal expected utility optimization on ﬁnite time hori-
zon and the risk-sensitive portfolio optimization on ﬁnite and inﬁnite time horizon.
We obtain optimal portfolios in relevant cases. A numerical procedure is also devel-
oped to compute the optimal expected terminal utility for ﬁnite horizon problem.
Keywords Risk-sensitive control · Semi-Markov process · Fixed income securities ·
We study a portfolio optimization problem in continuous time for a portfolio con-
sisting of n + 1 securities. One of them is a locally risk free money market account
with a ﬂoating interest rate which is governed by a semi-Markov process and the
other n(≥ 1) are risky assets, assumed to follow semi-Markov modulated geomet-
ric Brownian motions. The risky assets represent stocks or some security derivatives.
There is considerable literature on portfolio optimization problem beginning with
This work was supported in part by a DST project: SR/S4/MS: 379/06; also supported in part by a
grant from UGC via DSA-SAP Phase IV, and in part by a CSIR Fellowship.
M.K. Ghosh (
) · A. Goswami
Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
Department of Mathematics, Indian Institute of Technology Bombay, Mumbai 76, India