Trading a Mean-Reverting Asset with Regime Switching: An Asymptotic Approach
This chapter is concerned with an optimal trading rule. The underlying asset price is governed by a mean-reverting model with regime switching. In particular, the equilibrium levels are dependent of a two-state Markov chain so that the underlying process always moves around its current equilibrium. The objective is to buy and sell the asset so as to maximize the overall return. In this chapter we consider the case in which the jump rates of the Markov chain go to infinite and study the asymptotic properties of the corresponding value functions. We establish the convergence of the value functions to those of a limiting problem, which is easier to solve. In addition, the solution of the limiting problem is used to construct a trading rule which is shown via a numerical example to be nearly optimal.
KeywordsStock Price Viscosity Solution Asymptotic Property Regime Switching Geometric Brownian Motion
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