Proportional Transaction Costs in the Robust Control Approach to Option Pricing: The Uniqueness Theorem

Naïma El Farouq (1) , Pierre Bernhard (2)

1 LIMOS - Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes
2 BIOCORE - Biological control of artificial ecosystems

We prove the missing uniqueness theorem for the viscosity solution of a quasi-variational inequality related to a minimax impulse control problem modeling the option pricing with proportional transactions costs. This result makes our robust control approach of option pricing in the interval market model essentially complete.

Mots clés: viscosity solutions; robust control; Option pricing

Domaines: Automatique; Equations aux dérivées partielles [math.AP]; Pricing [q-fin.PR]

Naïma El Farouq, Pierre Bernhard. Proportional Transaction Costs in the Robust Control Approach to Option Pricing: The Uniqueness Theorem. Applied Mathematics and Optimization, 2015, 72 (2), pp.187-202. ⟨10.1007/s00245-014-9276-y⟩. ⟨hal-01090616⟩