zbMATH — the first resource for mathematics

Superreplication under gamma constraints. (English) Zbl 0960.91036
In a financial market with the underlying price process given by a Markovian Itō diffusion, this paper studies the problem of superreplicating a given payoff under a gamma constraint on the hedging strategy. This constraint imposes a boundedness condition on the space derivative of the hedging strategy or on the second space derivative of the pricing function. For the general case, the authors prove a verification theorem characterizing the superreplication cost as the solution of a quasi-variational inequality; this is then solved explicitly in the Black-Scholes model with constant coefficients. The main tools are a new dynamic programming principle and viscosity solution techniques.

91G10 Portfolio theory
60H30 Applications of stochastic analysis (to PDEs, etc.)
35K55 Nonlinear parabolic equations
49J20 Existence theories for optimal control problems involving partial differential equations
Full Text: DOI