# Arbitrage-Free Markets and the Pricing Kernel

Chapter

## Abstract

One of the basic assumptions in finance is that markets are free of arbitrage possibilities Since arbitrage implies the creation of wealth out of nothing, it seems obvious that such possibilities should be rare in financial markets. Thus, our theoretical approach assumes that markets are arbitrage-free For the technical definition of arbitrage-free markets let us first introduce the market setting.

## Keywords

Asset Price Trading Strategy Risky Asset Price Kernel Equivalent Martingale Measure
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## Notes

- 1.The analysis in this Chapter can be easily extended to n-dimensional Brownian motions However, little more insights would be gained at the cost of a more difficult notation.Google Scholar
- 2.See Karatzas and Shreve [109].Google Scholar
- 3.For detailed discussions of trading strategies see Bingham and Kiesel [15] pp 172 and Musiela and Rutkowski [145] pp 112.Google Scholar
- 4.See for example Musiela and Rutkowski [145], p 15, p 247 and Bingham and Kiesel [15] p 87 and p 174.Google Scholar
- 5.For a more detailed discussion of the Radon-Nikodym Theorem see for example Williams [187].Google Scholar
- 6.Since we will only consider forward pricing kernels for ease of notation we will omit the term “forward”.Google Scholar
- 7.See for example Bingham and Kiesel [15], pp 93.Google Scholar
- 9.Extensive discussions of diffusion processes are given in Karatzas and Shreve [109] and Musiela and Rutkowski [145] See also Cochrane [41] for a less technical discussion.Google Scholar
- 10.See Musiela and Rutkowski [145], p 467 and also Harrison and Kreps [90], pp. 396.Google Scholar
- 11.See Musiela and Rutkowski [145], p 466 and also Harrison and Kreps [90], pp. 397.Google Scholar
- 12.There is an extensive literature on the aggregation of investors in complete and especially in incomplete markets, see Constantinides [44], Geanakoplos [80], Gorman [84], Rubinstein [165] Comprehensive reviews are given in Huang, Litzenberger [99], Lewbel [120], Meyer [143], and Karatzas and Shreve [108].Google Scholar
- 14.This well known relationship is derived in many textbooks, see for example Cochrane [41], Pranke and Hax [72] or Ingersoll [101].Google Scholar
- 15.See Cochrane [41] and Pranke, Stapleton and Subrahmanyam [74].Google Scholar
- 16.For an extensive discussion see Camara [29] and Camara [30].Google Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 2004