On a stochastic differential equation arising in a price impact model
Peter Bank (Technische Universit\"at Berlin), Dmitry Kramkov, (Carnegie Mellon, Oxford)
TL;DR
This paper establishes conditions for the existence and uniqueness of solutions to a stochastic differential equation related to a price impact model, focusing on utility functions and Malliavin differentiability.
Contribution
It introduces sufficient conditions based on smoothness, boundedness, and Malliavin calculus for solving a key SDE in price impact modeling.
Findings
Provided criteria for solution existence and uniqueness
Linked utility functions and Malliavin differentiability to SDE solvability
Enhanced understanding of mathematical conditions in price impact models
Abstract
We provide sufficient conditions for the existence and uniqueness of solutions to a stochastic differential equation which arises in a price impact model. These conditions are stated as smoothness and boundedness requirements on utility functions or Malliavin differentiability of payoffs and endowments.
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