Viscosity solution of system of integro-partial differential equations with interconnected obstacles of non-local type without Monotonicity Conditions
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| Main Authors: | , , |
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| Format: | Preprint |
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2019
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| _version_ | 1866914932297039872 |
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| author | Hamadène, Said Mnif, Mohamed Neffati, Sarah |
| author_facet | Hamadène, Said Mnif, Mohamed Neffati, Sarah |
| contents | In this paper, we study a system of second order integro-partial differential equations with interconnected obstacles with non-local terms, related to an optimal switching problem with the jump-diffusion model. Getting rid of the monotonicity condition on the generators with respect to the jump component, we construct a continuous viscosity solution which is unique in the class of functions with polynomial growth. In our study, the main tool is the notion of reflected backward stochastic differential equations with jumps with interconnected obstacles for which we show the existence of a solution. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1905_05426 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Viscosity solution of system of integro-partial differential equations with interconnected obstacles of non-local type without Monotonicity Conditions Hamadène, Said Mnif, Mohamed Neffati, Sarah Analysis of PDEs 60H30 In this paper, we study a system of second order integro-partial differential equations with interconnected obstacles with non-local terms, related to an optimal switching problem with the jump-diffusion model. Getting rid of the monotonicity condition on the generators with respect to the jump component, we construct a continuous viscosity solution which is unique in the class of functions with polynomial growth. In our study, the main tool is the notion of reflected backward stochastic differential equations with jumps with interconnected obstacles for which we show the existence of a solution. |
| title | Viscosity solution of system of integro-partial differential equations with interconnected obstacles of non-local type without Monotonicity Conditions |
| topic | Analysis of PDEs 60H30 |
| url | https://arxiv.org/abs/1905.05426 |