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Financial Models in One Period Economy

  • Peter Carr
  • Qiji Jim Zhu
Chapter
  • 653 Downloads
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

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.

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    Zhu, Q.J.: Convex analysis in mathematical finance. Nonlinear Anal. Theory Methods Appl. 75, 1719–1736 (2012)CrossRefGoogle Scholar

Copyright information

© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Peter Carr
    • 1
  • Qiji Jim Zhu
    • 2
  1. 1.Department of Finance and Risk EngineeringTandon School of Engineering, New York UniversityNew YorkUSA
  2. 2.Department of MathematicsWestern Michigan UniversityKalamazooUSA

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