Recently it has been pointed out that there exists an isomorphism between the asset pricing formula of the fixed income instruments and the complementary distribution function of reliability and survival analysis. The aim of this dissertation is to exploit this isomorphism beyond that which has already been done. In doing so, we have been able to consider issues in mathematical finance that have not been considered before. In particular, we have proposed new families of stochastic processes for the forward interest rate function, have advocated a consideration of stochastic processes for the integrated forward interest rate function, have drawn attention to the special nuances and caveats that the statistical and inferential issues spawned by problems of mathematical finance, and have shown how some modern non-parametric Bayes procedures used in life-data analysis can be fruitfully invoked in the context of asset pricing. The highlights of our contribution pertain to a use of the hitting times of certain stochastic processes to random barriers, interest rate modeling via the newly proposed Beta processes and a use of the Dirichlet and the Neutral to the Right Processes for designing investment strategies that involve the pooling of information from several agents.
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