Topics in pricing American type financial contracts

In this thesis we study three pricing problems related to American type financial contracts: firstly, we derive a closed form upper bound for American put options. This upper bound can be used in conjunction with traditional Monte Carlo simulation, which usually generates a lower bound, to obtain a better estimate for the option price; secondly, we solve an optimal control problem and derive an optimal strategy for the owner of a stock which is subject to default risk; thirdly, we prove an ordering result for American options with a piecewise linear payoff under a family of equivalent martingale measures used in stochastic volatility models

Application of rough sets technique in resource selection problem

In this paper a resource selection problem is studied. We analyze the properties of the resource selection problem and propose some criteria for a good resource selection model. A simple-minded model, a traditional rough set model, a generalized rough set (GRS) model, and a high-order rough set (HORS) model are introduced and the advantages and disadvantages of each model are compared. It is shown that the HORS model is superior to other models except that it is much more time consuming. Some methods to reduce the complexity of the HORS model are also proposed