Portfolio optimization under a quantile hedging constraint
We study a problem of portfolio optimization under a European quantile hedging constraint. More precisely, we consider a class of Markovian optimal stochastic control problems in which two controlled processes must meet a probabilistic shortfall constraint at some terminal date. We denote by V the c...
| Main Author: | |
|---|---|
| Format: | Journal article |
| Published: |
World Scientific Publishing
2018
|
| _version_ | 1797095954822725632 |
|---|---|
| author | Bouveret, G |
| author_facet | Bouveret, G |
| author_sort | Bouveret, G |
| collection | OXFORD |
| description | We study a problem of portfolio optimization under a European quantile hedging constraint. More precisely, we consider a class of Markovian optimal stochastic control problems in which two controlled processes must meet a probabilistic shortfall constraint at some terminal date. We denote by V the corresponding value function. Following the arguments introduced in the literature on stochastic target problems, we convert this problem into a state constraint one in which the constraint is defined by means of an auxiliary value function v characterizing the reachable set. This set is therefore not given a priori but is naturally integrated in v solving, in a viscosity sense, a nonlinear parabolic partial differential equation (PDE). Relying on the existing literature, we derive, in the interior of the domain, a Hamilton–Jacobi–Bellman characterization of V. However, v involves an additional controlled state variable coming from the diffusion of the probability of reaching the target and belonging to the compact set [0,1]. This leads to nontrivial boundaries for V that must be discussed. Our main result is thus the characterization of V at those boundaries. We also provide examples for which comparison results exist for the PDE solved by V on the interior of the domain. |
| first_indexed | 2024-03-07T04:35:22Z |
| format | Journal article |
| id | oxford-uuid:cfbd3eca-5953-4017-83e0-efdafd3f65fe |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:35:22Z |
| publishDate | 2018 |
| publisher | World Scientific Publishing |
| record_format | dspace |
| spelling | oxford-uuid:cfbd3eca-5953-4017-83e0-efdafd3f65fe2022-03-27T07:44:49ZPortfolio optimization under a quantile hedging constraintJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:cfbd3eca-5953-4017-83e0-efdafd3f65feSymplectic Elements at OxfordWorld Scientific Publishing2018Bouveret, GWe study a problem of portfolio optimization under a European quantile hedging constraint. More precisely, we consider a class of Markovian optimal stochastic control problems in which two controlled processes must meet a probabilistic shortfall constraint at some terminal date. We denote by V the corresponding value function. Following the arguments introduced in the literature on stochastic target problems, we convert this problem into a state constraint one in which the constraint is defined by means of an auxiliary value function v characterizing the reachable set. This set is therefore not given a priori but is naturally integrated in v solving, in a viscosity sense, a nonlinear parabolic partial differential equation (PDE). Relying on the existing literature, we derive, in the interior of the domain, a Hamilton–Jacobi–Bellman characterization of V. However, v involves an additional controlled state variable coming from the diffusion of the probability of reaching the target and belonging to the compact set [0,1]. This leads to nontrivial boundaries for V that must be discussed. Our main result is thus the characterization of V at those boundaries. We also provide examples for which comparison results exist for the PDE solved by V on the interior of the domain. |
| spellingShingle | Bouveret, G Portfolio optimization under a quantile hedging constraint |
| title | Portfolio optimization under a quantile hedging constraint |
| title_full | Portfolio optimization under a quantile hedging constraint |
| title_fullStr | Portfolio optimization under a quantile hedging constraint |
| title_full_unstemmed | Portfolio optimization under a quantile hedging constraint |
| title_short | Portfolio optimization under a quantile hedging constraint |
| title_sort | portfolio optimization under a quantile hedging constraint |
| work_keys_str_mv | AT bouveretg portfoliooptimizationunderaquantilehedgingconstraint |