271ccda8-715b-4a8a-a712-f7bfd297a84520250313080343219wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON SYSTEMS2224-26781109-277710.37394/23202http://wseas.org/wseas/cms.action?id=40671220241220242310.37394/23202.2024.23https://wseas.com/journals/systems/2024.phpMarioLefebvreDepartment of Mathematics and Industrial Engineering, Polytechnique Montréal, 2500, chemin de Polytechnique, Montréal (Québec) H3T 1J4, CANADAA homing problem for a one-dimensional Bessel diffusion process is considered. The aim is to bring the controlled process to a value representing ground level as quickly as possible while taking the control costs into account. The cost function includes a parameter that takes the risk sensitivity of the optimizer into account. An explicit solution is found for both the value function and the optimal control in a particular problem.123120241231202451752053https://wseas.com/journals/systems/2024/b085102-035(2024).pdf10.37394/23202.2024.23.53https://wseas.com/journals/systems/2024/b085102-035(2024).pdfM. Lefebvre, LQG homing problems for processes used in financial mathematics, Revue Roumaine de Mathématiques Pures et Appliquées, Vol. 63, 2018, pp. 27–37. P. Whittle, Optimization over Time, vol. I. Chichester (UK): Wiley, 1982. P. Whittle, Risk-Sensitive Optimal Control, Chichester (UK): Wiley, 1990. 10.1109/9.83548R. Rishel, Controlled wear process: modeling optimal control, IEEE Transactions on Automatic Control, Vol. 36, No. 9, 1991, pp. 1100–1102. DOI: 10.1109/9.83548. 10.1007/s11009-020-09800-2M. Kounta and N. J. Dawson, Linear quadratic Gaussian homing for Markov processes with regime switching and applications to controlled population growth/decay, Methodology and Computing in Applied Probability, Vol. 23, 2021, pp. 1155–1172. DOI: 10.1007/s11009- 020-09800-2. 10.1109/tac.2022.3157077C. Makasu, Homing problems with control in the diffusion coefficient, IEEE Transactions on Automatic Control, Vol. 67, No. 7, 2022, pp. 3770–3772. DOI: 10.1109/TAC.2022.3157077. 10.1016/j.automatica.2024.111575C. Makasu, Bounds for a risk-sensitive homing problem, Automatica, Vol. 163, 2024, 111575. https://doi.org/10.1016/j.automatica.2024.1115 75. R. Bellman, Dynamic Programming, Princeton, NJ: Princeton University Press, 1957. S. Karlin and H. M. Taylor, A Second Course in Stochastic Processes, New York: Academic Press, 1981. 10.2307/3213947J. Kuhn, The risk-sensitive homing problem, Journal of Applied Probability, Vol. 22, No. 4, 1985, pp. 796–803. DOI: 10.2307/3213947.