arXiv subjects

Kensuke Ishitani

Publications and source records attributed to Kensuke Ishitani.

9 recordsLinked to original sources

arXiv2026

Pattern block method for generating random numbers : Reformulation and generalization of the Ziggurat method using conditional random variables

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 generalization of the Ziggurat method. The pattern block method enables the generation of random numbers from multimodal density functions and multidimensional distributions. The effectiveness of the pattern block method is demonstrated through several examples.

math.PR↗

arXiv2025

Construction and sample path properties of diffusion house-moving between two curves

The purpose of this paper is to introduce the construction of a stochastic process called ``diffusion house-moving'' and to explore its properties. We study the weak convergence of diffusion bridges conditioned to stay between two curves, and we refer to this limit as diffusion house-moving. Applying this weak convergence result, we give the sample path properties of diffusion house-moving.

math.PR↗

arXiv2024

Higher order integration by parts formulae for Wiener measures on a path space between two curves

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 integration by parts formulae introduce nontrivial boundary terms, unlike the first-order one. Furthermore, in the process of proving these formulae, it becomes necessary to employ the construction methods of Brownian excursion and Brownian house-moving through random walk approximations. To express the integration by parts formula concisely, we introduced a notation called Symmetrization. This notation enables the rewriting of the intricate expressions of boundary terms associated with higher-order integration by parts into more concise forms. Additionally, we provided a probabilistic explanation for the boundary terms by introducing symbols based on the concept of infinitesimal probability. These efforts are aimed at fostering an intuitive understanding of the integration by parts formulae.

math.PR↗

arXiv2024

On the weak convergence of conditioned Bessel bridges

The purpose of this paper is to introduce the construction of a stochastic process called "$δ$-dimensional Bessel house-moving" and its properties. We study the weak convergence of $δ$-dimensional Bessel bridges conditioned from above, and we refer to this limit as $δ$-dimensional Bessel house-moving. Applying this weak convergence result, we give the decomposition formula for its distribution and the Radon-Nikodym density for the distribution of the Bessel house-moving with respect to the one of the Bessel process. We also prove that $δ$-dimensional Bessel house-moving is a $δ$-dimensional Bessel process hitting a fixed point for the first time at $t=1$.

math.PR↗

arXiv2020

Construction and sample path properties of Brownian house-moving between two curves

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, statements are prepared on the weak convergence of conditioned Brownian motions, conditioned Brownian bridges, and conditioned three-dimensional Bessel bridges. Moreover, the sample path properties of Brownian house-moving are studied as well.

math.PR↗

arXiv2016

Computation of first-order Greeks for barrier options using chain rules for Wiener path integrals

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 type and with time-dependent trigger levels. In particular, we develop chain rules for Wiener path integrals between two curves that arise in the computation of first-order Greeks for barrier options. We also illustrate the effectiveness of our method through numerical examples.

q-fin.MF↗

arXiv2016

Effects of randomization on asymptotic periodicity of nonsingular transformations

It is known that the Perron--Frobenius operators of piecewise expanding $\mathcal{C}^2$ transformations possess an asymptotic periodicity of densities. On the other hand, external noise or measurement errors are unavoidable in practical systems; therefore, all realistic mathematical models should be regarded as random iterations of transformations. This paper aims to discuss the effects of randomization on the asymptotic periodicity of densities.

math.DS↗

arXiv2015

Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact

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 impact as the limit of a discrete-time value function. Here, we investigate some properties of the derived value function. In particular, we show that the function is continuous and has the semigroup property, which is strongly related to the Hamilton-Jacobi-Bellman quasi-variational inequality. Moreover, we show that noise in market impact causes risk-neutral assessment to underestimate the impact cost. We also study typical examples under a log-linear/quadratic market impact function with Gamma-distributed noise.

q-fin.TR↗

arXiv2015

Mathematical Formulation of an Optimal Execution Problem with Uncertain Market Impact

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 execution. Market impact is formulated as the product of a deterministic part increasing with execution volume and a positive stochastic noise part. Then, we derive a continuous-time model as a limit of a discrete-time value function. We find that the continuous-time value function is characterized by a stochastic control problem with a Levy process.

q-fin.TR↗