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

Lépinette, Emmanuel; Vu, Duc Thinh (2023), Dynamic programming principle and computable prices in financial market models with transaction costs., Journal of Mathematical Analysis and Applications, 54, 2. 10.1016/j.jmaa.2023.127068

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Type
Article accepté pour publication ou publié
Date
2023
Journal name
Journal of Mathematical Analysis and Applications
Volume
54
Number
2
Publisher
Elsevier
Publication identifier
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Author(s)
Lépinette, Emmanuel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Vu, Duc Thinh
Faculty of Sciences of Tunis [University of Tunis]
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