Financial Models in One Period Economy

Abstract

This chapter focuses on financial models in a one period economy with a finite sample space. Mathematically, these models involve only finite dimensional spaces yet they still illustrate the main patterns.

In modeling the behavior of agents in a financial market, we usually use concave utility functions and convex risk measure to characterize their attitude towards risk. These agents are subject to various constraints ranging from the availability of capital, contractual obligation to clients to mandates from regulators. Thus, the theory regarding constrained (convex) optimization discussed in the previous chapter is most relevant. The Lagrange multipliers in such financial models often carry a special financial meaning and are worthy of attention. Moreover, as illustrated in the previous chapter, they also provide the key link between the primal and the dual problems.