马尔可夫调制的几何布朗运动的最小熵鞅测度(英文)

The MEMMs for Markov-Modulated GBMs

本文中,我们考虑风险资产由马尔可夫调制的几何布朗运动驱动的期权定价问题.在此模型中,市场参数如市场利率、升值幅度和风险资产的波动率都依赖于不可观的经济状态,而这些经济状态是由连续时间隐马尔可夫链来描述.由马尔可夫调制的几何布朗运动描述的市场一般不是完备的,因此鞅测度不唯一.我们采用最小熵鞅测度作为马尔可夫调制的几何布朗运动模型的适宜的鞅测度,并且得到了一般意义上的最小熵鞅测度.

In this paper, we consider the option pricing problem when the risky underlying assets are driven by Markov-modulated geometric Brownian motion （GBM）. That is, the market parameters, for instance, the market interest rate, the appreciation rate and the volatility of the risky asset, depend on unobservable states of the economy which are modeled by a continuous-time hidden Markov chain. The market described by the Markov-modulated GBM model is incomplete in general, and, hence, the martingale measure is not unique. We adopt the minimal relative entropy martingale measure （MEMM） for the Markov-modulated GBM model as the suitable martingale measure and we obtain the MEMM for the market in general sense.