|Publication ahead of print|
|Published online||07 June 2018|
A risk-sensitive maximum principle for a Markov regime-switching jump-diffusion system and applications
School of Mathematics, Sun Yat-sen University,
510275, People’s Republic of China
2 Actuarial Science Program, Department of Mathematics, Morgan State University, Maryland 21251, USA
3 African Institute for Mathematical Sciences, University of Ghana, Ghana
4 Institute for Financial and Actuarial Mathematics, Department of Mathematics, University of Liverpool, L69 7ZL, United Kingdom
a Corresponding author: email@example.com
Revised: 8 March 2017
Accepted: 21 May 2017
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.
Mathematics Subject Classification: 93E20 / 91G80
Key words: Risk-sensitive control / Regime-switching / Jump-diffusion / Stochastic maximum principle / Asset management
© EDP Sciences, SMAI 2018
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.