Abstract
We consider the problem of optimal multiple switching in a finite horizon when the state of the system, including the switching costs, is a general adapted stochastic process. The problem is formulated as an extended impulse control problem and solved using probabilistic tools such as the Snell envelope of processes and reflected backward stochastic differential equations. Finally, when the state of the system is a Markov process, we show that the associated vector of value functions provides a viscosity solution to a system of variational inequalities with interconnected obstacles.
Original language | English (US) |
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Pages (from-to) | 2751-2770 |
Number of pages | 20 |
Journal | SIAM Journal on Control and Optimization |
Volume | 48 |
Issue number | 4 |
DOIs | |
State | Published - 2009 |
Keywords
- Backward stochastic differential equations
- Impulse control
- Optimal switching
- Real options
- Snell envelope
- Stopping time
- Variational inequalities
ASJC Scopus subject areas
- Control and Optimization
- Applied Mathematics