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Convergence of Optimal Expected Utility for a Sequence of Discrete-Time Markets in Initially Enlarged Filtrations

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  • Geoff Lindsell

Abstract

In this paper, we extend Kreps' conjecture that optimal expected utility in the classic Black-Scholes-Merton (BSM) economy is the limit of optimal expected utility for a sequence of discrete-time economies in initially enlarged filtrations converge to the BSM economy in an initially enlarged filtration in a "strong" sense. The n-th discrete-time economy is generated by a scaled n-step random walk, based on an unscaled random variable with mean 0, variance 1, and bounded support. Moreover, the informed insider knows each functional generating the enlarged filtrations path-by-path. We confirm Kreps' conjecture in initially enlarged filtrations when the consumer's utility function U has asymptotic elasticity strictly less than one.

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  • Geoff Lindsell, 2022. "Convergence of Optimal Expected Utility for a Sequence of Discrete-Time Markets in Initially Enlarged Filtrations," Papers 2203.08859, arXiv.org, revised Mar 2022.
    • Handle: RePEc:arx:papers:2203.08859
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    References listed on IDEAS

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    1. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 263-286, July.
    2. Amendinger, Jürgen, 2000. "Martingale representation theorems for initially enlarged filtrations," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 101-116, September.
    3. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," SFB 373 Discussion Papers 1998,25, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Baudoin, Fabrice, 0. "Conditioned stochastic differential equations: theory, examples and application to finance," Stochastic Processes and their Applications, Elsevier, vol. 100(1-2), pages 109-145, July.
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