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Dynamic programming principle and computable prices in financial market models with transaction costs

Lépinette, Emmanuel; Vu, Duc Tinh (2021), Dynamic programming principle and computable prices in financial market models with transaction costs. https://basepub.dauphine.psl.eu/handle/123456789/22224

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-03284655
Date
2021
Series title
Cahier de recherche du CEREMADE
Pages
38
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Author(s)
Lépinette, Emmanuel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Vu, Duc Tinh
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
How to compute (super) hedging costs in rather general financial market models with transaction costs in discrete-time ? Despite the huge literature on this topic, most of results are characterizations of the super-hedging prices while it remains difficult to deduce numerical procedure to estimate them. We establish here a dynamic programming principle and we prove that it is possible to implement it under some conditions on the conditional supports of the price and volume processes for a large class of market models including convex costs such as order books but also non convex costs, e.g. fixed cost models.
Subjects / Keywords
Hedging costs; European options; Dynamic programming principle; No-arbitrage condition; AIP condition; Random set theory; Lower semicontinuity