On an aggregate state-price deflator in a multi-period market model

In this paper, we study arbitrage theory in a basic multi-period market model. Malamud and Trubowitz (Math Financ Econ 1(2): 129–161, 2007) used an aggregate state-price deflator and an orthogonal projection onto the payoff subspace to describe the recursive structure of optimal consumption streams....

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Bibliographic Details
Published in:Japan journal of industrial and applied mathematics 2021-09, Vol.38 (3), p.1063-1074
Main Author: Adachi, Takashi
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Martingales
Mathematics
Mathematics and Statistics
Original Paper
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Summary:In this paper, we study arbitrage theory in a basic multi-period market model. Malamud and Trubowitz (Math Financ Econ 1(2): 129–161, 2007) used an aggregate state-price deflator and an orthogonal projection onto the payoff subspace to describe the recursive structure of optimal consumption streams. We present explicit expressions of these instruments. We also prove that the density process of a unique minimal martingale measure, with respect to an original measure, can be the aggregate state-price deflator in a market discounted by a numeraire.
ISSN:0916-7005
1868-937X
DOI:10.1007/s13160-021-00476-w