On the Weak Convergence of Conditioned Bessel Bridges

J. Math. Sci. Univ. Tokyo
Vol. 30 (2023), No. 3, Page 287–339.

Ishitani, Kensuke; Rin, Tokufuku; Yanashima, Shun
On the Weak Convergence of Conditioned Bessel Bridges
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The purpose of this paper is to introduce the construction of a stochastic process called $``\delta$-dimensional Bessel house-moving$"$ and its properties. We study the weak convergence of $\delta$-dimensional Bessel bridges conditioned from above, and we refer to this limit as $\delta$-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 $\delta$-dimensional Bessel house-moving is a $\delta$-dimensional Bessel process hitting a fixed point for the first time at $t=1$.

Keywords: Barrier options, Greeks, Bessel bridge, Bessel house-moving.

Mathematics Subject Classification (2020): Primary 60F17; Secondary 60J25.
Received: 2022-11-29