State price density (SPD) and stochastic discount factor (SDF) are important elements in asset pricing. In this thesis, I first propose to use projection pursuit regression (PPR) and local polynomial regression (LPR) to estimate the SPD of interest rates nonparametrically. By using a similar approach, I also estimate the delta values in the interest rate options and discusses how to delta-hedge these options. Unlike SPD measured in a risk-neutral economy, SDF is implied by an asset pricing model. It displays which prices are reasonable given the returns in the current period. Hansen and Jagannathan (1997) develop the Hansen-Jagannathan distance (HJ-distance) to measure pricing errors produced by SDF. While the HJ-distance has several desirable properties, Ahn and Gadarowski (2004) find that the specification test based on the HJ-distance overrejects correct models too severely in commonly used sample size to provide a valid test. This thesis proposes to improve the finite sample properties of the HJ-distance test by applying the shrinkage method (Ledoit and Wolf, 2003) to compute its weighting matrix. / Thesis (Ph.D, Economics) -- Queen's University, 2008-06-19 00:00:55.996

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This thesis discusses the financial market model with proportional transaction costs considered in Cvitanic and Karatzas (1996) (hereafter we use CK (1996)). For a modified dual problem introduced by Choulli (2009), I discuss solutions under weaker conditions than those of CK (1996), and furthermore the obtained solutions generalize the examples treated in CK (1996). Then, I consider the exponential utility which does not belong to the family of utility considered by CK (1996) due to the Inada condition. Finally, I elaborate the same results as in CK (1996) for the exponential utility, and I derive other related results using the specificity of the exponential utility function as well. These lead to a different method/approach than CK (1996) for our utility maximization problem, and different notion of admissibility for financial strategies as well. / Mathematical Finance