Well-Posedness and Comparison Principle for Option Pricing with Switching Liquidity
Tihomir Gyulov, Lyuben Valkov
TL;DR
This paper analyzes an integro-differential equation modeling European option pricing under liquidity shocks, establishing well-posedness and a comparison principle to ensure solution stability and uniqueness.
Contribution
It introduces a novel mathematical framework for option pricing with liquidity shocks, proving well-posedness and comparison principles for the associated integro-differential equation.
Findings
Proved well-posedness of the model.
Established a comparison principle for solutions.
Provided mathematical validation for option pricing under liquidity shocks.
Abstract
We consider an integro-differential equation derived from a system of coupled parabolic PDE and an ODE which describes an European option pricing with liquidity shocks. We study the well-posedness and prove comparison principle for the corresponding initial value problem.
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