9 papers
Pattern block method for generating random numbers : Reformulation and generalization of the Ziggurat method using conditional random variables
Kensuke Ishitani
The Ziggurat method is an efficient rejection sampling technique for generating one-dimensional normally distributed random numbers. This study proposes the pattern block method, a…
Construction and sample path properties of diffusion house-moving between two curves
Kensuke Ishitani, Soma Nishino
This study aims to construct a stochastic process called ``diffusion house-moving,'' which is a diffusion bridge conditioned to stay between its starting point and its ending point…
Higher order integration by parts formulae for Wiener measures on a path space between two curves
Kensuke Ishitani, Soma Nishino
We have formulated higher-order integration by parts formulae on the path space restricted between two curves, with respect to pinned/ordinary Wiener measures. The higher-order int…
On the weak convergence of conditioned Bessel bridges
Kensuke Ishitani, Tokufuku Rin, Shun Yanashima
The purpose of this paper is to introduce the construction of a stochastic process called "-dimensional Bessel house-moving" and its properties. We study the weak convergence of…
Construction and sample path properties of Brownian house-moving between two curves
Kensuke Ishitani, Daisuke Hatakenaka, Keisuke Suzuki
This study aims to construct a stochastic process called "Brownian house-moving," which is a Brownian bridge conditioned to stay between two curves. To construct this process, stat…
Computation of first-order Greeks for barrier options using chain rules for Wiener path integrals
Kensuke Ishitani
This paper presents a new methodology to compute first-order Greeks for barrier options under the framework of path-dependent payoff functions with European, Lookback, or Asian typ…
Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact
Kensuke Ishitani, Takashi Kato
This paper is a continuation of Ishitani and Kato (2015), in which we derived a continuous-time value function corresponding to an optimal execution problem with uncertain market i…
Effects of randomization on asymptotic periodicity of nonsingular transformations
Hiroshi Ishitani, Kensuke Ishitani
It is known that the Perron--Frobenius operators of piecewise expanding transformations possess an asymptotic periodicity of densities. On the other hand, external…
Mathematical Formulation of an Optimal Execution Problem with Uncertain Market Impact
Kensuke Ishitani, Takashi Kato
We study an optimal execution problem with uncertain market impact to derive a more realistic market model. We construct a discrete-time model as a value function for optimal execu…