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    Multiperiod pricing theory

    Olufodun, Adetokunbo Lukuman (2021) Multiperiod pricing theory. PhD thesis, Birkbeck, University of London.

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    Abstract

    We extend the methodology proposed by Carr, Geman and Madan [11] for pricing and hedging in incomplete markets to more general probability spaces and prove a result, which shows the equivalence between the notion of the absence of strictly acceptable opportunities and the existence of a representative state pricing function. We also give examples of how to construct valuation test measures. We also extend the methodology to the discrete-time setting with a finite time horizon. We specify a finite set of single-period probability measures at each non-terminating node of a tree, which are then used to generate a set of probability measures for the entire tree by pasting together these single-period measures across all the nodes. We define the concept of a strictly acceptable opportunity in this new framework and state a result, which gives the condition that guarantees the absence of strictly acceptable opportunities. We also consider a Lucas-type pure exchange economy (see [37]) consisting of N infinitely long-lived agents, who have access to the same information regarding the stochastic evolution of a process. However, these agents do not interpret the information in the same way. We work in a continuous-time model as discussed in Brown and Rogers [10]. Further, we assume that the agents have a homogeneous coefficient of relative risk aversion. We then give a characterisation of the equilibrium, which does not depend on any form of the utility function. Thereafter, we assume that each agent has a power utility function, and we obtain concrete results for the price of the traded asset. We also obtain an expression for the agent's wealth process and give the dynamics of the state-price density and the asset price.

    Metadata

    Item Type: Thesis
    Copyright Holders: The copyright of this thesis rests with the author, who asserts his/her right to be known as such according to the Copyright Designs and Patents Act 1988. No dealing with the thesis contrary to the copyright or moral rights of the author is permitted.
    Depositing User: Acquisitions And Metadata
    Date Deposited: 18 Nov 2021 14:16
    Last Modified: 18 Nov 2021 14:16
    URI: https://eprints.bbk.ac.uk/id/eprint/46759

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