Multilevel particle filters for Lévy-driven stochastic differential equations
| Autor: | Prince Peprah Osei, Ajay Jasra, Kody J. H. Law |
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| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Physics Discretization 010103 numerical & computational mathematics 01 natural sciences Lévy process Theoretical Computer Science 010104 statistics & probability Stochastic differential equation Computational Theory and Mathematics Applied mathematics Continuum (set theory) 0101 mathematics Statistics Probability and Uncertainty Particle filter Path dependent |
| Zdroj: | Statistics and Computing. 29:775-789 |
| ISSN: | 1573-1375 0960-3174 |
| DOI: | 10.1007/s11222-018-9837-z |
| Popis: | We develop algorithms for computing expectations with respect to the laws of models associated to stochastic differential equations driven by pure Levy processes. We consider filtering such processes as well as pricing of path dependent options. We propose a multilevel particle filter to address the computational issues involved in solving these continuum problems. We show via numerical simulations and theoretical results that under suitable assumptions regarding the discretization of the underlying driving Levy proccess, the cost to obtain MSE $$\mathcal {O}(\epsilon ^2)$$ scales like $$\mathcal {O}(\epsilon ^{-2})$$ for our method, as compared with the standard particle filter $$\mathcal {O}(\epsilon ^{-3})$$ . |
| Databáze: | OpenAIRE |
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