ABSTRACT We propose a dividend stock valuation model where multiple dividend growth series and their dependencies are modelled using a multivariate Markov chain. Our model advances existing Markov chain stock models. First, we determine assumptions that guarantee the finiteness of the price and risk as well as the fulfilment of transversality conditions. Then, we compute the first- and second-order price-dividend ratios by solving corresponding linear systems of equations and show that a different price-dividend ratio is attached to each combination of states of the dividend growth process of each stock. Subsequently, we provide a formula for the computation of the variances and covariances between stocks in a portfolio. Finally, we apply the theoretical model to the dividend series of three US stocks and perform comparisons with existing models. The results could also be applied for actuarial purposes as a general stochastic investment model and for calculating the initial endowment to fund a portfolio of dependent perpetuities.

中文翻译：

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多元马尔可夫链库存模型

摘要 我们提出了一种股息股票估值模型，其中使用多元马尔可夫链对多个股息增长序列及其相关性进行建模。我们的模型改进了现有的马尔可夫链库存模型。首先，我们确定保证价格和风险的有限性以及满足横向条件的假设。然后，我们通过求解相应的线性方程组来计算一阶和二阶市盈率，并表明不同的市盈率被附加到每只股票的股息增长过程的每种状态组合。随后，我们提供了计算投资组合中股票之间的方差和协方差的公式。最后，我们将理论模型应用于三只美股的股息序列，并与现有模型进行比较。