Malliavin calculus for marked binomial processes: portfolio optimisation in the trinomial model and compound Poisson approximation
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866913428974600192 |
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| author | Halconruy, Hélène |
| author_facet | Halconruy, Hélène |
| contents | In this paper we develop a stochastic analysis for marked binomial processes, that can be viewed as the discrete analogues of marked Poisson processes. The starting point is the statement of a chaotic expansion for square-integrable (marked binomial) functionals, prior to the elaboration of a Markov-Malliavin structure within this framework. We take advantage of the new formalism to deal with two main applications. First, we revisit the Chen-Stein method for the (compound) Poisson approximation which we perform in the paradigm of the built Markov-Malliavin structure, before studying in the second one the problem of portfolio optimisation in the trinomial model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_00914 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Malliavin calculus for marked binomial processes: portfolio optimisation in the trinomial model and compound Poisson approximation Halconruy, Hélène Probability 60G55, 60H07, 60B10 G.3 In this paper we develop a stochastic analysis for marked binomial processes, that can be viewed as the discrete analogues of marked Poisson processes. The starting point is the statement of a chaotic expansion for square-integrable (marked binomial) functionals, prior to the elaboration of a Markov-Malliavin structure within this framework. We take advantage of the new formalism to deal with two main applications. First, we revisit the Chen-Stein method for the (compound) Poisson approximation which we perform in the paradigm of the built Markov-Malliavin structure, before studying in the second one the problem of portfolio optimisation in the trinomial model. |
| title | Malliavin calculus for marked binomial processes: portfolio optimisation in the trinomial model and compound Poisson approximation |
| topic | Probability 60G55, 60H07, 60B10 G.3 |
| url | https://arxiv.org/abs/2104.00914 |