The basic theory of the arbitrage pricing theory finance essay

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The basic theory of the arbitrage pricing theory finance essay

Taychang Wang, University of Pennsylvania Abstract This dissertation consists of five essays on the theory of arbitrage pricing. A bound on the pricing errors is obtained.

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This bound is similar to the bound obtained by Ross and Huberman More generally, it is shown that when idiosyncratic risks are not strongly dependent or when the sequence of the idiosyncratic risks is a lacunary systemthe approximate linear pricing relation still holds.

It is demonstrated that the models in HubermanIngersoll and Chamberlain and Rothschild are all special cases of this one.

The basic theory of the arbitrage pricing theory finance essay

It is also proved that, under suitable assumptions on the linear factor structure, the linear pricing relation implies the nonexistence of asymptotic arbitrage opportunities.

Thus the no-asymptotic-arbitrage position is a necessary and sufficient condition for the approximate linear relation.

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Finally, It is established that the APT is still correct after any linear transformation as long as the product of the transformation matrix and its transpose is uniformly bounded.

This whole exercise is necessary since different definitions of the no-asymptotic-arbitrage condition usually work for different types of utility functions which is the main result of the second essay.

The definition of dispersion depends on the context we are interested in. The relation between mimicking portfolios and exact arbitrage is also investigated in a way similar to Huberman, Kandel, and Stambaugh Box and Cox () developed the transformation.

Estimation of any Box-Cox parameters is by maximum likelihood.

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Box and Cox () offered an example in which the data had the form of survival times but the underlying biological structure was of hazard rates, and the transformation identified this. Essays on the theory of arbitrage pricing.

Taychang Wang, University of Pennsylvania. Abstract. This dissertation consists of five essays on the theory of arbitrage pricing.^ The first essay derives the APT when the second central absolute moments (variances) of the assets returns do not exist.

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The basic theory of the arbitrage pricing theory finance essay

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The Basic Theory Of The Arbitrage Pricing Theory Finance Essay