Super-hedging an arbitrary number of European options with integer-valued strategies

Dorsaf Cherif (1) , Meriam El Mansour (2) , Emmanuel Lépinette (2)

1 FST - Faculté des Sciences Mathématiques, Physiques et Naturelles de Tunis
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

The usual theory of asset pricing in finance assumes that the financial strategies, i.e. the quantity of risky assets to invest, are realvalued so that they are not integer-valued in general, see the Black and Scholes model for instance. This is clearly contrary to what it is possible to do in the real world. Surprisingly, it seems that there is no contribution in that direction in the literature. In this paper, we show that, in discrete-time, it is possible to evaluate the minimal super-hedging price when we restrict ourselves to integer-valued strategies. To do so, we only consider terminal claims that are continuous piecewise affine functions of the underlying asset. We formulate a dynamic programming principle that can be directly implemented on an historical data and which also provides the optimal integer-valued strategy.

Mots clés: Super-hedging prices; European options; Integer- valued strategies; Optimal super-hedging prices; Dynamic programming principle

Domaines: Probabilités [math.PR]

Dorsaf Cherif, Meriam El Mansour, Emmanuel Lépinette. Super-hedging an arbitrary number of European options with integer-valued strategies. 2022. ⟨hal-03835027⟩