科研之友
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摘要
This paper is concerned with a finite-horizon optimal selling rule problem when the underlying stock price movements are modeled by a Markov switching L谷vy process. Assuming that the transaction fee of the selling operation is a function of the underlying stock price, the optimal selling rule can be obtained by solving an optimal stopping problem. The corresponding value function is shown to be the unique viscosity solution to the associated HJB variational inequalities. A numerical example is presented to illustrate the results. 1. Introduction One of the major decision investors have to make on a daily basis is to identify the best time to sell or buy a particular stock. Usually if the right decision is not taken at the right time, this will generally result in large losses for the investor. Such decisions are mainly affected by various macro- and micro-economical parameters. One of the main factors that affect decision making in the marketplace is the trend of the stock market. In this paper, we study trading decision making when we assume that market trends are subject to change and that these fluctuations can be captured by a combination of a latent Markov chain and a jump process. In fact, we model the stock price dynamics with a regime switching L谷vy process. Regime switching L谷vy processes are obtained by combining a finite number of geometric L谷vy processes modulated by a finite-state Markov chain. This type of processes clearly capture the main features of a wide variety of stock such as energy stock and commodities which usually display a lot of spikes and seasonality. Selling rule problems in general have been intensively studied in the literature, and most of the work have been done when the stock price follows a geometric Brownian motion or a simple Markov switching process. Among many others, we can cite the work of Zhang [1]; in this paper, a selling rule is determined by two threshold levels, and a target price and a stop-loss limit are considered. One makes a selling decision whenever the price reaches either the target price or the stop-loss limit. The objective is to choose these threshold levels to maximize an expected return function. In [1], such optimal threshold levels are obtained by solving a set of two-point boundary value problems. Recently Pemy and Zhang [2] studied a similar problem in the case where there is no jump process associated and the underlying dynamics is just a traditional Markov switching process built by coupling a set of geometric Brownian motions. In this paper, we extend the result of Pemy and Zhang [2],
