2015/04/14 by Daniel Hernández–Hernández, José Luis Pérez, Hernandez-Hernandez, Daniel +3
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #49J40 #60G51 #93E20 #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1504.03496
openalex publication_date 2015/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We revisit a stochastic control problem of optimally modifying the underlying spectrally negative Levy process. A strategy must be absolutely continuous with respect to the Lebesgue measure, and the objective is to minimize the total costs of the running and controlling costs. Under the assumption that the running cost function is convex, we show the optimality of a refraction strategy. We also obtain the convergence of the optimal refraction strategies and the value functions, as the control set is enlarged, to those in the relaxed case without the absolutely continuous assumption. Numerical results are further given to confirm these analytical results.