On the Weak Convergence of Conditioned Bessel Bridges
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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Abstract:
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.
Mathematical Reviews Number: MR4665163
Received: 2022-11-29
