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Valuation in Incomplete Markets

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IV market problem generalizing earlier results of Duffie and Richardson (1991)[DR91]. There have been multiple attempts to theoretically pick one for pricing purpose according to different optimal criteria, some of which are related to utility maximization. For instance, the Föllmer-Schweizer minimal measure by Föllmer and Schweizer (1991)[FS91]. As we can see the hedging of derivatives in incomplete financial markets is a frequently studied problem in mathematical finance. Several different approaches have been developed in literature, but no agreement on one uniformly superior method has emerged so far. The purpose of this thesis is to review two quadratic hedging approaches really interesting in the incomplete market literature: local risk-minimization and mean-variance hedging; and a minimal martingale measure approach. In a nutshell, the main difference between these two approaches is the following: one has either simple solution for hedging strategies (local risk- minimization) or a control over total cost and risks (mean-variance hedging), but not both. The thesis is structured as follows. We first explain in Section 1 the general theoretical background of complete markets. Section 2 explains the importance and the difference between martingale, semimartingale, local semi-martingale and quadratic function, in order to proceed and better understand the different approaches. In Section 3 we give some preliminaries definitions and then in section 4, we explain the local risk-minimization theory, the minimal martingale measure approach and the mean-variance hedging. In Section 5 we study a particular case of incompleteness: due to information. In section 6 we give our conclusion on the argument.

Anteprima della Tesi di Luca Cassani

Anteprima della tesi: Valuation in Incomplete Markets, Pagina 2

Tesi di Laurea

Facoltà: Scienze economiche statistiche e sociali

Autore: Luca Cassani Contatta »

Composta da 129 pagine.

 

Questa tesi ha raggiunto 760 click dal 05/05/2005.

 

Consultata integralmente 6 volte.

Disponibile in PDF, la consultazione è esclusivamente in formato digitale.