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A bang-bang strategy for a finite fuel stochastic control problem
- Part of
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- Journal:
- Advances in Applied Probability / Volume 24 / Issue 3 / September 1992
- Published online by Cambridge University Press:
- 01 July 2016, pp. 589-603
- Print publication:
- September 1992
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- Article
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The problem treated is that of controlling a process
with values in [0, a]. The non-anticipative controls (µ(t), σ(t)) are selected from a set C(x) whenever X(t–) = x and the non-decreasing process A(t) is chosen by the controller subject to the condition 
where y is a constant representing the initial amount of fuel. The object is to maximize the probability that X(t) reaches a. The optimal process is determined when the function 
has a unique minimum on [0, a] and satisfies certain regularity conditions. The optimal process is a combination of ‘timid play' in which fuel is used gradually in the form of local time at 0, and ‘bold play' in which all the fuel is used at once.
where 
has a unique minimum on [0, 