Risk sensitive control of finite state Markov chains in discrete time, with applications to portfolio management

1999 ◽  
Vol 50 (2) ◽  
pp. 167-188 ◽  
Author(s):  
Tomasz Bielecki ◽  
Daniel Hernández-Hernández ◽  
Stanley R. Pliska
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Portfolio Management ◽  
Risk Sensitive ◽  
Finite State ◽  
Risk Sensitive Control

On quasi-stationary distributions in absorbing continuous-time finite Markov chains

1967 ◽  
Vol 4 (1) ◽  
pp. 192-196 ◽  
Author(s):  
J. N. Darroch ◽  
E. Seneta
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Continuous Time ◽  
Present Note ◽  
Time Parameter ◽  
Stationary Distributions ◽  
Finite State ◽  
Absorbing Markov Chains ◽  
Finite Markov Chains ◽  
Finite State Space

In a recent paper, the authors have discussed the concept of quasi-stationary distributions for absorbing Markov chains having a finite state space, with the further restriction of discrete time. The purpose of the present note is to summarize the analogous results when the time parameter is continuous.

scholarly journals Robust control of discrete-time hybrid systems with uncertain modal dynamics

2004 ◽  
Vol 2004 (3) ◽  
pp. 197-208 ◽  
Author(s):  
Thordur Runolfsson
Keyword(s):  
Markov Chain ◽  
Disturbance Rejection ◽  
Structural Changes ◽  
External Disturbance ◽  
Operational Mode ◽  
Cost Functional ◽  
Risk Sensitive ◽  
Finite State ◽  
Risk Sensitive Control ◽  
Modal Dynamics

We study systems that are subject to sudden structural changes due to either changes in the operational mode of the system or failure. We consider linear dynamicalsystems that depend on a modal variable which is either modeled as a finite-state Markov chain or generated by an automaton that is subject to an external disturbance. In the Markov chain case, the objective of the control is to minimize a risk-sensitive cost functional. The risk-sensitive cost functional measures the risk sensitivity of the system to transitions caused by the random modal variable. In the case when a disturbed automaton describes the modal variable, the objective of the control is to make the system as robust to changes in the external disturbance as possible. Optimality conditions for both problems are derived and it is shown that the disturbance rejection problem is closely related to a certain risk-sensitive control problem for the hybrid system.

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