Abstract
AbstractWe consider an optimal switching problem where the terminal reward depends on the entire control trajectory. We show existence of an optimal control by applying a probabilistic technique based on the concept of Snell envelopes. We then apply this result to solve an impulse control problem for stochastic delay differential equations driven by a Brownian motion and an independent compound Poisson process. Furthermore, we show that the studied problem arises naturally when maximizing the revenue from operation of a group of hydro-power plants with hydrological coupling.
Publisher
Springer Science and Business Media LLC
Subject
Management Science and Operations Research,General Mathematics,Software
Reference26 articles.
1. Agram N, Øksendal B (2019) Stochastic control of memory mean-field processes. Appl Math Optim 79:181–204
2. Aïd R, Campi L, Langrené N, Pham H (2014) A probabilistic numerical method for optimal multiple switching problems in high dimension. SIAM J Financ Math 5(1):191–231
3. Aslaksen I, Bjerkholt O, Brekke KA, Lindstrøm T, Øksendal B (1990) The choice between hydro and thermal power generation under uncertainty. In: Bjerkholt O, Olsen Ø, Vislie J (eds) Recent modelling approaches in applied energy economics. Chapman and Hall, London, pp 187–205
4. Aslaksen I, Bjerkholt O, Brekke KA, Lindstrøm T, Øksendal B (1993) A class of solvable stochastic investment problems involving singular controls. Stochastics 43:29–63
5. Brekke KA, Øksendal B (1994) Optimal switching in an economic activity under uncertainty. SIAM J Control Optim 32(4):1021–1036
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献