摘要：This paper is concerned with the Black–Scholes–Barenblatt equation ∂ t u + r ( x ∂ x u − u ) + G ( x 2 ∂ x x u ) = 0 $\partial _{t}u+r(x\partial _{x}u-u)+G(x^,\partial _{xx}u)=0$ , where G ( α ) = 1 2 ( σ ‾ 2 − σ _ 2 ) | α | + 1 2 ( σ ‾ 2 + σ _ 2 ) α $G(\alpha )=\frac),(\overline{\sigma}^,-\underline{\sigma}^,)|\alpha |+\frac),(\overline{\sigma}^,+\underline{\sigma}^,)\alpha $ , α ∈ R $\alpha \in \mathbb{R}$ . This equation is usually used for derivative pricing in the financial market with volatility uncertainty. We discuss a strict comparison theorem for Black–Scholes–Barenblatt equations, and study strict sub-additivity of their solutions with respect to terminal conditions.
