| dc.contributor.author | Elie, Romuald | |
| dc.date.accessioned | 2010-02-18T11:07:31Z | |
| dc.date.available | 2010-02-18T11:07:31Z | |
| dc.date.issued | 2009 | |
| dc.identifier.uri | https://basepub.dauphine.fr/handle/123456789/3504 | |
| dc.language.iso | en | en |
| dc.subject | Quantile Constraint | en |
| dc.subject | Dynamic Programming Equation | en |
| dc.subject | Stochastic Target Problem | en |
| dc.subject.ddc | 519 | en |
| dc.subject.classificationjel | C73 | en |
| dc.title | Quantile hedging and optimal control under stochastic target constraints | en |
| dc.type | Communication / Conférence | |
| dc.description.abstracten | We consider the problem of finding the minimal initial data of a controlled process which guarantees
to reach a controlled target with a given probability of success or, more generally, with a given level of
expected loss. By suitably increasing the state space and the controls, we show that this problem can
be converted into a stochastic target problem, i.e. find the minimal initial data of a controlled process
which guarantees to reach a controlled target with probability one. Unlike the existing literature on
stochastic target problems, our increased controls are valued in an unbounded set. In this paper, we
provide a new derivation of the dynamic programming equation for general stochastic target problems
with unbounded controls, together with the appropriate boundary conditions. These results are applied
to the problem of quantile hedging in financial mathematics, and are shown to recover the explicit
solution of Follmer and Leukert. We then consider the problem of miximizing a utility function under
this type of quantile constraint. The previous study allows to characterize the domain in which the
value fuction lies and we provide an Hamilton-Jacobi-Bellman representation of the associated value
function. Contrary to standard state constraint problems, the domain is not given a-priori and we do
not need to impose conditions on its boundary. | en |
| dc.description.sponsorshipprivate | oui | en |
| dc.subject.ddclabel | Probabilités et mathématiques appliquées | en |
| dc.relation.conftitle | Istanbul Workshop on Mathematical Finance | en |
| dc.relation.confdate | 2009-05 | |
| dc.relation.confcity | Istanbul | en |
| dc.relation.confcountry | Turquie | en |
