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Liquidity and optimal consumption with random income
Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab). (Financial Mathematics)
Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
2011 (engelsk)Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
Abstract [en]

In the first part of our work we focus on the model of the optimal consumption with a random income. We provide the three dimensional equation for this model, demonstrate the reduction to the two dimensional case and provide for two different utility functions the full point-symmetries' analysis of the equations. We also demonstrate that for the logarithmic utility there exists a unique and smooth viscosity solution the existence of which as far as we know was never demonstrated before.

In the second part of our work we develop the concept of the empirical liquidity measure. We provide the retrospective view of the works on this issue, discuss the proposed definitions and develop our own empirical measure based on the intuitive mathematical model and comprising several features of the definitions that existed before. Then we verify the measure provided on the real data from the market and demonstrate the advantages of the proposed value for measuring the illiquidity.

sted, utgiver, år, opplag, sider
2011.
Emneord [en]
Financial Mathematics, HJB equation, liquidity, optimal consumption, random income
HSV kategori
Identifikatorer
URN: urn:nbn:se:hh:diva-16108Lokal ID: IDE1149OAI: oai:DiVA.org:hh-16108DiVA, id: diva2:438569
Fag / kurs
Financial Mathematics
Presentation
2011-05-27, Wigrforssalen, Kristian IV:s väg 3, Halmstad, 16:45 (engelsk)
Uppsök
Physics, Chemistry, Mathematics
Veileder
Examiner
Tilgjengelig fra: 2011-09-03 Laget: 2011-09-03 Sist oppdatert: 2011-09-06bibliografisk kontrollert

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