Stochastic Fluid Models with Positive Jumps at Level Zero

Hédi Nabli ()
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Hédi Nabli: University of Sfax

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 1, 289-308

Abstract: 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.

Keywords: Markov process; Stochastic fluid models; Partial differential equations; MSC 60J25; MSC 60J75; MSC 60K15 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-021-09852-y

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