In this paper, we derive a general stochastic maximum principle for a risk-sensitive type optimal control problem of Markov regime-switching jump-diffusion model. The results are obtained via a logarithmic transformation and the relationship between adjoint variables and the value function. We apply the results to study both a linear-quadratic optimal control problem and a risk-sensitive benchmarked asset management problem for Markov regime-switching models. In the latter case, the optimal control is of feedback form and is given in terms of solutions to a Markov regime-switching Riccatti equation and an ordinary Markov regime-switching differential equation.
Accepté le :
DOI : 10.1051/cocv/2017039
Keywords: Risk-sensitive control, Regime-switching, Jump-diffusion, Stochastic maximum principle, Asset management
Sun, Zhongyang 1 ; Kemajou-Brown, Isabelle 1 ; Menoukeu-Pamen, Olivier 1
@article{COCV_2018__24_3_985_0,
author = {Sun, Zhongyang and Kemajou-Brown, Isabelle and Menoukeu-Pamen, Olivier},
title = {A risk-sensitive maximum principle for a {Markov} regime-switching jump-diffusion system and applications},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {985--1013},
year = {2018},
publisher = {EDP Sciences},
volume = {24},
number = {3},
doi = {10.1051/cocv/2017039},
mrnumber = {3877190},
zbl = {1405.93234},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2017039/}
}
TY - JOUR AU - Sun, Zhongyang AU - Kemajou-Brown, Isabelle AU - Menoukeu-Pamen, Olivier TI - A risk-sensitive maximum principle for a Markov regime-switching jump-diffusion system and applications JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 985 EP - 1013 VL - 24 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2017039/ DO - 10.1051/cocv/2017039 LA - en ID - COCV_2018__24_3_985_0 ER -
%0 Journal Article %A Sun, Zhongyang %A Kemajou-Brown, Isabelle %A Menoukeu-Pamen, Olivier %T A risk-sensitive maximum principle for a Markov regime-switching jump-diffusion system and applications %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 985-1013 %V 24 %N 3 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2017039/ %R 10.1051/cocv/2017039 %G en %F COCV_2018__24_3_985_0
Sun, Zhongyang; Kemajou-Brown, Isabelle; Menoukeu-Pamen, Olivier. A risk-sensitive maximum principle for a Markov regime-switching jump-diffusion system and applications. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 3, pp. 985-1013. doi: 10.1051/cocv/2017039
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