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Financial Markets in the Context of the General Theory of Optional Processes

In: Mathematical and Computational Approaches in Advancing Modern Science and Engineering

Author

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  • M. N. Abdelghani

    (University of Alberta)

  • A. V. Melnikov

    (University of Alberta)

Abstract

A probability space is considered “unusual” if the information flow is not right or left continuous or is not complete. On these probability spaces lives certain type of stochastic processes known as optional processes including optional semimartingales. Optional semimartingales have right and left limits but are not necessarily right or left continuous. Here, we present a short summary of the calculus of optional processes and define stochastic logarithms and present some of its properties. Moreover, we develop a financial market model based on optional semimartingales and methods for finding local martingale deflators for this market. Finally, we present some financial examples.

Suggested Citation

  • M. N. Abdelghani & A. V. Melnikov, 2016. "Financial Markets in the Context of the General Theory of Optional Processes," Springer Books, in: Jacques Bélair & Ian A. Frigaard & Herb Kunze & Roman Makarov & Roderick Melnik & Raymond J. Spiteri (ed.), Mathematical and Computational Approaches in Advancing Modern Science and Engineering, pages 519-528, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-30379-6_47
    DOI: 10.1007/978-3-319-30379-6_47
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