Abstract
Stability of the utility maximization problem with random endowment and indifference prices is studied for a sequence of financial markets in an incomplete Brownian setting. Our novelty lies in the nonequivalence of markets, in which the volatility of asset prices (as well as the drift) varies. Degeneracies arise from the presence of nonequivalence. In the positive real line utility framework, a counterexample is presented showing that the expected utility maximization problem can be unstable. A positive stability result is proved for utility functions on the entire real line.
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Notes
Many thanks to an anonymous reviewer for making this keen observation.
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The author would like to thank Dmitry Kramkov, Steve Shreve, Kasper Larsen and the anonymous reviewers for their constructive comments and suggestions.
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Weston, K. Stability of utility maximization in nonequivalent markets. Finance Stoch 20, 511–541 (2016). https://doi.org/10.1007/s00780-016-0289-z
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DOI: https://doi.org/10.1007/s00780-016-0289-z