Analysis of Jump Processes and Its Application to Optimal Control

2004 ◽  
Author(s):  
Yasushi Ishikawa
Keyword(s):  
Optimal Control ◽  
Jump Processes

scholarly journals Generalisation of Hajek’s Stochastic Comparison Results to Stochastic Sums

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Jörg Kampen
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Jump Processes ◽  
Control Problems ◽  
Stochastic Comparison ◽  
Comparison Result ◽  
Comparison Results ◽  
General Data ◽  
Passport Options

Hajek’s univariate stochastic comparison result is generalised to multivariate stochastic sum processes with univariate convex data functions and for univariate monotonic nondecreasing convex data functions for processes with and without drift, respectively. As a consequence strategies for a class of multivariate optimal control problems can be determined by maximizing variance. An example is passport options written on multivariate traded accounts. The argument describes a narrow path between impossibilities of generalisations to jump processes or impossibilities of more general data functions.

Optimal Control of Jump Processes

1977 ◽  
Vol 15 (1) ◽  
pp. 92-119 ◽  
Author(s):  
R. Boel ◽  
P. Varaiya
Keyword(s):  
Optimal Control ◽  
Jump Processes
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