Markovian structure of the Volterra Heston model
| Autor: | Eduardo Abi Jaber, Omar El Euch |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
010102 general mathematics Structure (category theory) Markov process 01 natural sciences Heston model Stochastic partial differential equation 010104 statistics & probability symbols.namesake symbols State space Applied mathematics Uniqueness Affine transformation 0101 mathematics Statistics Probability and Uncertainty Representation (mathematics) Mathematics |
| Zdroj: | Statistics & Probability Letters. 149:63-72 |
| ISSN: | 0167-7152 |
| DOI: | 10.1016/j.spl.2019.01.024 |
| Popis: | We characterize the Markovian and affine structure of the Volterra Heston model in terms of an infinite-dimensional adjusted forward process and specify its state space. More precisely, we show that it satisfies a stochastic partial differential equation and displays an exponentially-affine characteristic functional. As an application, we deduce an existence and uniqueness result for a Banach-space valued square-root process and provide its state space. This leads to another representation of the Volterra Heston model together with its Fourier–Laplace transform in terms of this possibly infinite system of affine diffusions. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect