Basket options have long been an important structured product. Although basket options have been extensively studied in the literature, there are few published papers that deal with the pricing of basket options with stochastic interest rates. This study presents two novel basket option pricing models that permit the interest rates to be random. The paper presents a powerful calculation technique for the problem when underlying stock returns are continuous. Finally, we use a regular grid method to the calculation of the formula of two-asset basket option when underlying stock returns are continuous and a mixture of both the regular grid method and a Monte Carlo method to the one when underlying stock returns are discontinuous, and sensitivity analyses are presented.

Based on a compound random process including geometric Brownian motion and Poisson process, we established a model which can describe the environmental uncertainty more flexible. And then, we use a stochastic optimal control model to address the issue of resource allocation. Our study conclusions indicate the following: (1) if rare events can be described using a Poisson process, then the fixed-point theorem can be used to solve resource allocation scheme; and (2) if a certain asset or a certain department’s facing a rare event leads to a reduction in value, then the rare event will not only affect investment in this asset or department but will also have ramifications for investment in related assets or departments. After that, we briefly discuss the resource allocation issues of financial institutions and manufacturing enterprises. The results show that the uncertain, flexible environmental of financial institutions can improve the efficiency of asset allocation. Manufacturing companies can respond effectively and positively to such uncertainty through a flexible asset allocation strategy. The contribution of our paper lies mainly in its use of new methods to describe uncertainty. When we re-define the environment of uncertainty, the flexible resource allocation scheme can effectively mitigate the impact of random adverse effects of the environment. In addition, if the description methods are closer to the facts themselves, then the scheme for flexibility in resource allocation may also bring about an excess return.