On the utility problem in a market where price impact is transient

L\'or\'ant Nagy and Mikl\'os R\'asonyi

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Abstract: We consider a discrete-time model of a financial market where a risky asset is bought and sold with transactions having a transient price impact. It is shown that the corresponding utility maximization problem admits a solution. We manage to remove some unnatural restrictions on the market depth and resilience processes that were present in earlier work. A non-standard feature of the problem is that the set of attainable portfolio values may fail the convexity property.

Date: 2025-11
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