BSDEs driven by time-changed Lévy noises and optimal control

2013/12/18 by Giulia Di Nunno, Di Nunno, Giulia, Steffen Sjursen +1
Economics, Econometrics and Finance · Mathematics · Social Sciences · #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Stochastic processes and financial applications #math.PR

paper · pdf · doi:10.48550/arxiv.1312.5120

arxiv created 2013/12/18 · openalex publication_date 2013/12/18 · arxiv updated 2013/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study backward stochastic differential equations (BSDEs) for time-changed Lévy noises when the time-change is independent of the Lévy process. We prove existence and uniqueness of the solution and we obtain an explicit formula for linear BSDEs and a comparison principle. BSDEs naturally appear in control problems. Here we prove a sufficient maximum principle for a general optimal control problem of a system driven by a time-changed Lévy noise. As an illustration we solve the mean-variance portfolio selection problem.

Citations

• Foundations of Modern Probability

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