Abstract
This paper is interested in studying a type of production models-stocks that can be seen as a stochastic fluid flow system with upward jumps at level zero. The joint distribution of the stocks level and the controlling Markov process is governed by two differential systems with specific boundary conditions. The uniqueness of the solution of this problem has been proved. Also, a unified solution with no distinction between singular or invertible drift matrix is proposed. The mathematical expectation is therefore derived. This method is based on the uniformization technique, which is acknowledged by its numerical stability and accuracy. A comparative study with a spectral-based solution is achieved to confirm this statement.
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Nabli, H. Stochastic Fluid Models with Positive Jumps at Level Zero. Methodol Comput Appl Probab 24, 289–308 (2022). https://doi.org/10.1007/s11009-021-09852-y
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DOI: https://doi.org/10.1007/s11009-021-09852-y