Next Article in Journal
Mortality Projections for Small Populations: An Application to the Maltese Elderly
Next Article in Special Issue
Imbalance Market Real Options and the Valuation of Storage in Future Energy Systems
Previous Article in Journal
A Deep Learning Integrated Lee–Carter Model
Previous Article in Special Issue
Dealing with Drift Uncertainty: A Bayesian Learning Approach
Open AccessArticle

Optimal Portfolio Selection in an Itô–Markov Additive Market

1
Department of Applied Mathematics, Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
2
Institute of Mathematics, Polish Academy of Sciences, 00-656 Warsaw, Poland
3
Vistula University, 02-787 Warsaw, Poland
4
Faculty of Management, Computer Science and Finance, Wrocław University of Economics, 53-345 Wrocław, Poland
*
Author to whom correspondence should be addressed.
Risks 2019, 7(1), 34; https://doi.org/10.3390/risks7010034
Received: 8 December 2018 / Revised: 12 March 2019 / Accepted: 18 March 2019 / Published: 25 March 2019
(This article belongs to the Special Issue Applications of Stochastic Optimal Control to Economics and Finance)
We study a portfolio selection problem in a continuous-time Itô–Markov additive market with prices of financial assets described by Markov additive processes that combine Lévy processes and regime switching models. Thus, the model takes into account two sources of risk: the jump diffusion risk and the regime switching risk. For this reason, the market is incomplete. We complete the market by enlarging it with the use of a set of Markovian jump securities, Markovian power-jump securities and impulse regime switching securities. Moreover, we give conditions under which the market is asymptotic-arbitrage-free. We solve the portfolio selection problem in the Itô–Markov additive market for the power utility and the logarithmic utility. View Full-Text
Keywords: Markov additive processes; Markov regime switching market; Markovian jump securities; asymptotic arbitrage; complete market; optimal portfolio Markov additive processes; Markov regime switching market; Markovian jump securities; asymptotic arbitrage; complete market; optimal portfolio
MDPI and ACS Style

Palmowski, Z.; Stettner, Ł.; Sulima, A. Optimal Portfolio Selection in an Itô–Markov Additive Market. Risks 2019, 7, 34.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop