A parabolic variational inequality arising from the valuation of strike reset options
The authors study a parabolic variational inequality problem \[ \begin{aligned} &\partial_t V-\frac{\sigma^2}2S^2\partial_{SS}V+rV\geq 0,\;V(S,\tau)\geq SP(\tau),\;S>0,\;0<\tau\leq T,\\ &\biggl[\partial_t V-\frac{\sigma^2}2S^2\partial_{SS}V+rV\biggr][V-SP(\tau)]=0,\;V(S,0)=(1-S)^+, \end{aligned} \] where \(V(S,\tau)\) is the option value. The paper establishes the existence and uniqueness of \(W_p^{1,2}\) solution and the boundedness and \(C^\infty\) smoothness of the free boundary. The monotonicity of the free boundary is proved in some situations.
scientific article; zbMATH DE number 5083417
scientific article