Quadratic expansions in optimal investment with respect to perturbations of the semimartingale model

Oleksii Mostovyi () and Mihai Sîrbu ()
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Oleksii Mostovyi: University of Connecticut
Mihai Sîrbu: The University of Texas at Austin

Finance and Stochastics, 2024, vol. 28, issue 2, No 7, 553-613

Abstract: Abstract We study the response of the optimal investment problem to small changes of the stock price dynamics. Starting with a multidimensional semimartingale setting of an incomplete market, we suppose that the perturbation process is also a general semimartingale. We obtain second-order expansions of the value functions, first-order corrections to the optimisers, and provide the adjustments to the optimal control that match the objective function up to the second order. We also give a characterisation in terms of the risk-tolerance wealth process, if it exists, by reducing the problem to the Kunita–Watanabe decomposition under a change of measure and numéraire. Finally, we illustrate the results by examples of base models that allow closed-form solutions, but where this structure is lost under perturbations of the model where our results allow an approximate solution.

Keywords: Asymptotic analysis; Semimartingale; Incomplete market; Duality theory; 93E20; 91G10; 91G15; 60H30 (search for similar items in EconPapers)
JEL-codes: C61 G11 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00780-024-00532-6

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