论文标题
通过使用功能性演算引入和求解广义的黑色choles PDE
Introducing and solving generalized Black-Scholes PDEs through the use of functional calculus
论文作者
论文摘要
我们介绍了一些涉及Riemann-Liouville和Weyl空间裂缝衍生物的广义黑色 - choles方程的家庭。我们证明，这些广义的黑色 - choles方程在$（l^1-l^\ infty）$ - 插值空间中均得到很好的体积。更确切地说，我们表明涉及这些方程式的椭圆类型运算符会产生全体形态的半群。然后，我们为相关解决方案提供明确的积分表达式。为了获得良好的方式，我们证明了在抽象环境中的双层操作员与部门运营商之间的新联系。这种联系将主题中的一些已知结果扩展到了运营商和所涉及功能的更广泛的家庭。
We introduce some families of generalized Black--Scholes equations which involve the Riemann-Liouville and Weyl space-fractional derivatives. We prove that these generalized Black--Scholes equations are well-posed in $(L^1-L^\infty)$-interpolation spaces. More precisely, we show that the elliptic type operators involved in these equations generate holomorphic semigroups. Then, we give explicit integral expressions for the associated solutions. In the way to obtain well-posedness, we prove a new connection between bisectorial operators and sectorial operators in an abstract setting. Such a connection extends some known results in the topic to a wider family of both operators and the functions involved.
