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Authors: Yin, G.

Article Type: Research Article

Abstract: This work aims to developing asymptotic expansions of solutions of a system of coupled differential equations with applications to option price under regime-switching diffusions. The main motivation stems from using switching diffusions to model stochastic volatility so as to obtain uniform asymptotic expansions of European-type options. By focusing on fast mean reversion, our effort is placed on finding the “effective volatility”. Under simple conditions, asymptotic expansions are developed with uniform asymptotic error bounds. The leading term in the asymptotic expansions satisfies a Black–Scholes equation in which the mean return rate and volatility are averaged out with respect to the stationary …measure of the switching process. In addition, the full asymptotic series is developed, which will help us to gain insight on the behavior of the option price when the time approaches maturity. The asymptotic expansions obtained in this paper are interesting in their own right and can be used for other problems in control optimization of systems involving fast varying switching processes. Show more

Keywords: asymptotic expansion, fast reversion, two-time scale

DOI: 10.3233/ASY-2009-0953

Citation: Asymptotic Analysis, vol. 65, no. 3-4, pp. 203-222, 2009

Authors: He, Qi | Yin, G.

Article Type: Research Article

Abstract: This work develops asymptotic properties of randomly switching and time inhomogeneous dynamic systems under Brownian perturbation with a small diffusion. The switching process is modeled by a continuous-time Markov chain, which portraits discrete events that cannot be modeled by a diffusion process. In the model, there are two small parameters. One of them is ε associated with the generator of the continuous-time, inhomogeneous Markov chain, and the other is δ=δε signifies the small intensity of the diffusion. Assume ε→0 and δε →0 as ε→0. This paper focuses on large deviations type of estimates for such Markovian switching systems with small …diffusions. The ratio ε/δε can be a nonzero constant, or equal to 0, or ∞. These three different cases yield three different outcomes. This paper analyzes the three cases and present the corresponding asymptotic properties. Show more

Keywords: large deviations, Markov chain, averaging principle

DOI: 10.3233/ASY-131198

Citation: Asymptotic Analysis, vol. 87, no. 3-4, pp. 123-145, 2014