Optimal Portfolio Selection in an Itô–Markov Additive Market
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: t...
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doaj-8091f41a82df47a296dc5ee3af5b71e32020-11-24T22:30:00ZengMDPI AGRisks2227-90912019-03-01713410.3390/risks7010034risks7010034Optimal Portfolio Selection in an Itô–Markov Additive MarketZbigniew Palmowski0Łukasz Stettner1Anna Sulima2Department of Applied Mathematics, Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, 50-370 Wrocław, PolandInstitute of Mathematics, Polish Academy of Sciences, 00-656 Warsaw, PolandFaculty of Management, Computer Science and Finance, Wrocław University of Economics, 53-345 Wrocław, PolandWe 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.https://www.mdpi.com/2227-9091/7/1/34Markov additive processesMarkov regime switching marketMarkovian jump securitiesasymptotic arbitragecomplete marketoptimal portfolio |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Zbigniew Palmowski Łukasz Stettner Anna Sulima |
spellingShingle |
Zbigniew Palmowski Łukasz Stettner Anna Sulima Optimal Portfolio Selection in an Itô–Markov Additive Market Risks Markov additive processes Markov regime switching market Markovian jump securities asymptotic arbitrage complete market optimal portfolio |
author_facet |
Zbigniew Palmowski Łukasz Stettner Anna Sulima |
author_sort |
Zbigniew Palmowski |
title |
Optimal Portfolio Selection in an Itô–Markov Additive Market |
title_short |
Optimal Portfolio Selection in an Itô–Markov Additive Market |
title_full |
Optimal Portfolio Selection in an Itô–Markov Additive Market |
title_fullStr |
Optimal Portfolio Selection in an Itô–Markov Additive Market |
title_full_unstemmed |
Optimal Portfolio Selection in an Itô–Markov Additive Market |
title_sort |
optimal portfolio selection in an itô–markov additive market |
publisher |
MDPI AG |
series |
Risks |
issn |
2227-9091 |
publishDate |
2019-03-01 |
description |
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. |
topic |
Markov additive processes Markov regime switching market Markovian jump securities asymptotic arbitrage complete market optimal portfolio |
url |
https://www.mdpi.com/2227-9091/7/1/34 |
work_keys_str_mv |
AT zbigniewpalmowski optimalportfolioselectioninanitomarkovadditivemarket AT łukaszstettner optimalportfolioselectioninanitomarkovadditivemarket AT annasulima optimalportfolioselectioninanitomarkovadditivemarket |
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1725742294587408384 |