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Optimal portfolio allocation by the martingale method in an incomplete and partially observable market
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2016 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Optimal portföljallokering genom martingalmetoden i en inkomplett och partiellt observerad marknad (Swedish)
Abstract [en]

In this thesis, we consider an agent who wants to maximize his expected utility of his terminal wealth with respect to the power utility by the martingale method. The assets that the agent can allocate his capital to are assumed to follow a stochastic differential equation and exhibits stochastic volatility. The stochastic volatility assumption will make the market incomplete and therefore, the martingale method will not have a unique solution. We resolve this issue by including fictitious assets that complete the market and solve the allocation problem in the completed market. From the optimal allocation in the completed market, we will adjust the drift parameter for the fictitious assets so that our allocation don't include the fictitious assets in the portfolio strategy. We consider also the case when the assets also has stochastic drift and the agent can only observe the price process, which makes the information in the market for the agent partially observable. Explicit results are presented for the full and partially observable case and a feedback solution is obtained in the full observable case when the asset and volatility are assumed to follow the Heston model.

Abstract [sv]

I denna uppsats har vi en individ som vill maximera sin förväntade nytta med avseende till en potens nyttofunktion med martingal metoden. De tillgångar som agenten kan fördela sitt kapital till antas följa en stokastisk differentialekvation och dessa tillgångar antar stokastisk volatilitet. Den stokastiska volatilitet göra att marknaden blir ofullständig och implicerar att martingal metoden inte kommer anta en unik lösning. Vi löser det problemet genom att inkludera fiktiva tillgångar som kompletterar marknaden och löser allokerings problem med martingal metoden i den nya fiktiva marknaden. Från den optimala allokeringen i den fiktiva marknaden, kommer vi att justera drift parametrarna för de fiktiva tillgångarna så att vår allokering inte inkluderar dem i portföljstrategin. Vi undersöker också fallet när tillgångarna har stokastisk drift och individen kan bara observera pris processen, vilket gör informationen på marknaden för individen delvis observerbar. Resultat presenteras för de fullt och delvis observerbara fallet och en lösning erhålls i det fullt observerbara fallet när tillgången och volatiliteten antas följa en Heston modell.

Place, publisher, year, edition, pages
2016.
Series
TRITA-MAT-E, 2016:51
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-190996OAI: oai:DiVA.org:kth-190996DiVA: diva2:954432
Subject / course
Mathematical Statistics
Educational program
Master of Science - Applied and Computational Mathematics
Supervisors
Examiners
Available from: 2016-08-22 Created: 2016-08-20 Last updated: 2016-08-22Bibliographically approved

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