  This paper is a continuation of Akahori-Barsotti-Imamura (2017) and where the
authors i) showed that a payment at a random time, which we call timing risk,
is decomposed into an integral of static positions of knock-in type barrier
options, ii) proposed an iteration of static hedge of a timing risk by
regarding the hedging error by a static hedge strategy of Bowie-Carr type with
respect to a barrier option as a timing risk, and iii) showed that the error
converges to zero by infinitely many times of iteration under a condition on
the integrability of a relevant function. Even though many diffusion models
including generic 1-dimensional ones satisfy the required condition, a
construction of the iterated static hedge that is applicable to any uniformly
elliptic diffusions is postponed to the present paper because of its
mathematical difficulty. We solve the problem in this paper by relying on the
symmetrization, a technique first introduced in Imamura-Ishigaki-Okumura (2014)
and generalized in Akahori-Imamura (2014), and also work on parametrix, a
classical technique from perturbation theory to construct a fundamental
solution of a partial differential equation. Due to a lack of continuity in the
diffusion coefficient, however, a careful study of the integrability of the
relevant functions is required. The long lines of proof itself could be a
contribution to the parametrix analysis.
