arXiv subjects

Kenji Yasutomi

Publications and source records attributed to Kenji Yasutomi.

4 recordsLinked to original sources

arXiv2021

Higher-order error estimates of the discrete-time Clark--Ocone formula

In this article, we investigate the convergence rate of the discrete-time Clark--Ocone formula provided by Akahori--Amaba--Okuma [1]. In that paper, they mainly focus on the $L_{2}$-convergence rate of the first-order error estimate related to the tracking error of the delta hedge in mathematical finance. Here, as two extensions, we estimate "the higher order error" for Wiener functionals with an integrability index $2$ and "an arbitrary differentiability index."

math.PR↗

arXiv2011

Random walk in a finite directed graph subject to a synchronizing road coloring

A constructive proof is given to the fact that any ergodic Markov chain can be realized as a random walk subject to a synchronizing road coloring. Redundancy (ratio of extra entropy) in such a realization is also studied.

math.PR↗

arXiv2010

Realization of finite-state mixing Markov chain as a random walk subject to a synchronizing road coloring

A mixing Markov chain is proved to be realized as a random walk in a directed graph subject to a synchronizing road coloring. The result ensures existence of appropriate random mappings in Propp--Wilson's coupling from the past. The proof is based on the road coloring theorem. A necessary and sufficient condition for approximate preservation of entropies is also given.

math.PR↗

arXiv2009

Asymptotic behavior of prices of path dependent options

In this paper, we give a numerical method for pricing long maturity, path dependent options by using the Markov property for each underlying asset. This enables us to approximate a path dependent option by using some kinds of plain vanillas. We give some examples whose underlying assets behave as some popular Levy processes. Moreover, we give some payoffs and functions used to approximate them.

q-fin.PR↗