In this paper, we study the pricing and hedging of catastrophe European option when catastrophe loss is described by a regime-switching jump di?usion process. We derive the close-form pricing formula of catastrophe European options and brie°y discuss the pricing issue of catastrophe bonds. We extend the formulas of static hedging strategies to the regime-switching setting and provide some discussions on the static hedging of catastrophe options. Numerical examples show that static hedging strategy of catastrophe options is effective.

This paper studies the dividend problem when the asset of the company is driven by a diffusion process and the dividend barrier follows a Markov process. The explicit expressions for dividends is derived and a numerical example is given.

Many articles agreed that it is possible for speculators to manipulate stock prices. In this article, we give a dynamic model to show in detail how one type of the trade-based manipulation is realized in stock markets, especially in emerging stock markets, where manipulators have dominative information and fund over the uninformed investors. In our model, we assume that uniformed investors predict future price movement with their forecasting model, the number of uniformed investors who decide to buy stocks increases with fitting degree of the forecasting model for past price data and the model parameters. With these assumptions, manipulators take two-step strategy (pumping the price and selling stocks at higher prices), the pumping step aims to absorb uninformed investors' following by buying the stock by use of the forecasting model, and the selling step is to sell all the stock in higher prices by trying their best to control the supplies and continually attracting the uniformed investors’ following. We show that manipulators can realize their strategies and maximize their final wealth by controlling the strength of pumping and deciding the time length to sell out the stocks. Two numerical examples are also given.