an:01519344
Zbl 0960.91036
Soner, H. Mete; Touzi, Nizar
Superreplication under gamma constraints
EN
SIAM J. Control Optimization 39, No. 1, 73-96 (2000).
00070769
2000
j
91G10 60H30 35K55 49J20
superreplication; gamma constraint; stochastic control; viscosity solution; stochastic analysis
In a financial market with the underlying price process given by a Markovian It?? 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.
Martin Schweizer (Berlin)