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Title: Quadratic expansions in optimal investment with respect to perturbations of the semimartingale model
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.  more » « less
Award ID(s):
1848339
PAR ID:
10499980
Author(s) / Creator(s):
;
Publisher / Repository:
Springer-Verlag GmbH Germany
Date Published:
Journal Name:
Finance and Stochastics
Volume:
28
Issue:
2
ISSN:
0949-2984
Page Range / eLocation ID:
553 to 613
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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