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Abstract
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I develop a theory for pricing in an incomplete market by assuming that the writer of a contingent claim requires compensation for the risk in the form of a pre-specified instantaneous Sharpe ratio. I focus on applying this idea to pricing a pure endowment in the presence of a stochastic hazard rate. In this talk, I intuitively derive the equation for the price and use a comparison principle to demonstrate many qualitative features of the price. In the Differential Equations seminar on 19 Oct, I will prove properties of the price for a collection of policyholders and determine the limit of the price per policyholder. This is joint work with Moshe Milevsky and David Promislow. |
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