Takuji Arai, Keio University

Title:   Shortfall risk based good-deal bounds for American derivatives

Abstract:
The aim of this talk is to obtain upper and lower bounds of good-deal bounds
induced by shortfall risk for American type derivatives.
For European type derivatives, these bounds are given through
shortfall risk measure, which is a convex risk measure.
Since an American derivative is described as a process,
we have to define a new type shortfall risk measure as a functional defined
on processes.
Moreover, we have to consider upper and lower bounds separately
when we treat American derivatives, that is,
we define shortfall risk measure from seller's view and one from buyer's view
individually.
I shall introduce some properties and representation results of these
shortfall risk measures for American derivatives.