ON NON-UNIQUENESS OF SOLUTIONS TO DEGENERATE PARABOLIC EQUATIONS IN THE CONTEXT OF OPTION PRICING IN THE HESTON MODEL

Battle Count: 97

The paper addresses a fundamental theoretical question about the uniqueness of option prices in the Heston model, which is one of the most widely used stochastic volatility models in quantitative finance. Understanding when option prices are uniquely determined (and hence arbitrage-free) is essential for any quantitative trading desk using the Heston model. However, the paper is purely theoretical and does not provide directly implementable trading strategies or numerical algorithms. Its relevance is primarily at the foundational/theoretical level for practitioners who need to understand the mathematical conditions under which Heston model prices are well-defined.

This is a purely theoretical mathematics paper with no computational implementation. The results are analytical proofs and explicit formulae. There is no code, algorithm, or numerical method to implement. The mathematical content requires advanced knowledge of PDE theory, Fichera function analysis, and Tikhonov-Täcklind uniqueness classes.

This is a purely theoretical mathematics paper with complete proofs and explicit formulae. All results are self-contained and verifiable through standard PDE theory. The key counterexample (equation 15) is given in closed form and can be directly verified by substitution into the PDE. No computational experiments or datasets are involved.