Mario Lefebvre, Romain Mrad, "First Exit and Optimization Problems for a CIR Diffusion Process," WSEAS Transactions on Mathematics, vol. 24, pp. 382-388, 2025, DOI:10.37394/23206.2025.24.36
Mario Lefebvre, Romain Mrad. First Exit and Optimization Problems for a CIR Diffusion Process.
WSEAS Transactions on Mathematics. 2025;24:382-388. 10.37394/23206.2025.24.36
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 24, 2025
First Exit and Optimization Problems for a CIR Diffusion Process
Authors: ,
Abstract: Let {X(t), t ≥ 0} be a CIR diffusion process, and τ (x) be the first time that X(t) = 0 or c, given that
X(0) = x ∈ (0, c). First, we compute the moment-generating function and the expected value of τ (x). Then, an
optimal control problem is considered for {X(t), t ≥ 0}. Finally, we add jumps to the diffusion process and we
calculate in a particular case the probability that X(τ (x)) = 0, as well as the expected time needed to leave the
interval (0, c). Explicit and exact results are obtained.
Keywords:
First-passage time, Brownian motion, Poisson process, uniform jumps, homing problem, integro-differential equation
Pages: 382-388 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 24, 2025, Art. #36 DOI: 10.37394/23206.2025.24.36
×
Citation Tools