Shingo Saito

Sum formula for finite multiple zeta values

The sum formula is one of the most well-known relations among multiple zeta values. This paper proves a conjecture of Kaneko predicting that an analogous formula holds for finite multiple zeta values.

The Bowman-Bradley theorem for multiple zeta-star values

Abstract Text The Bowman–Bradley theorem asserts that the multiple zeta values at the sequences obtained by inserting a fixed number of twos between 3 , 1 , … , 3 , 1 add up to a rational multiple of a power of π. We establish its counterpart for multiple zeta-star values by showing an identity in a non-commutative polynomial algebra introduced by Hoffman. Video For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=LpqA2OJ6vP8 .

Knot points of typical continuous functions

It is well known that most continuous functions are nowhere differentiable. Furthermore, in terms of Dini derivatives, most continuous functions are nondifferentiable in the strongest possible sense except in a small set of points. In this paper, we completely characterise families

Introduction to the Premium Principle Based on the Wang Transform

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Applicability of Bayesian Methods for Loss Ratio Estimation

of sets of points for which most continuous functions have the property that such small set of points belongs to

Generalisation of Mack's formula for claims reserving with arbitrary exponents for the variance assumption

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Bowman-Bradley type theorem for finite multiple zeta values

. The proof uses a topological zero-one law and the Banach-Mazur game.

Asymptotic tail dependence of the normal copula

This is a self-contained introductory survey article on the premium principle based on the Wang transform. We give the definition and examples of the Wang transform and prove that the induced premium principle is a coherent risk measure.

Bayesian approach to measuring parameter and model risk in loss ratio estimation

In an earlier paper, we proposed a Bayesian approach towards estimating the Value-at-Risk of an insurance loss ratio, taking into account both the parameter risk and the model risk. In this paper, we apply the approach to real data and evaluate the plausibility of the estimators.