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This paper is based on our paper [15]. We present the main results; the verbatim proofs are omitted due to the page limitation. We develop large deviations principles for systems driven by continuous-time Markov chains with two-time scales and related optimal control problems. A distinct feature of our setup is that the Markov chain under consideration is time dependent or inhomogeneous. The use of...
This paper considers option pricing under a regime-switching model. The switching process takes two different modes, and the underlying stock price evolves in accordance with the two modes dictated by a continuous-time, 2-state Markov chain. At a given instance, the price follows either a model of geometric Brownian motion or mean-reversion model on its market mode. We build stochastic approximation...
This paper focuses on option pricing using a stochastic optimization algorithm. The underlying stock price changes according to a set of geometric Brownian motions coupled by a continuous- time finite state Markov chain. A recursive stochastic optimization algorithm is constructed to estimate the implied volatility. Convergence analysis of the algorithm is provided together with rate of convergence...
We develop a filtering scheme for hybrid systems with the process dictating the system configuration being a finite-state Markov chain. Exploiting hierarchical structure of the underlying system, the states of the Markov chain are divided into a number of groups so that it jumps rapidly within each group and slowly among different groups. Focusing on reduction of computational complexity, the filtering...
As most computer systems are expected to remain operational 24 hours a day, 7 days a week, they must complete maintenance work while in operation. This work is in addition to the regular tasks of the system and its purpose is to improve system reliability and availability. Nonetheless, additional work in the system, although labeled as best effort or low priority, still affects the performance of...
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