Convex risk measure

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  • In everyday life we are often forced to make decisions involving risks and perceived opportunities. The consequences of our decisions are affected by the outcomes of random variables that are to various degrees beyond our control. Such decision problems arise, for instance, in financial and insurance markets.

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  • Throughout this paper, we consider a valuation method for contingent claims taking control of shortfall risk into account in the framework of complete market models. After giving a general form of the valuation, we shall deal with models whose underlying assets are described by diffusion processes, and obtain a result for American type claims

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  • As a matter of sound investment practice, FHLBanks should be able to measure the price sensitivity for individual securities and for the entire portfolio. In general, techniques used to measure the risk of individual securities are also appropriate for the entire portfolio. To estimate portfolio sensitivity, FHLBanks generally use, at a minimum, duration. Because of the presence of options in most portfolios, duration may not be an effective risk measure.

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  • Topic 12 - Measuring and managing interest rate risk with financial forwards, futures and swaps. In this chapter, students can understand and can recall how DV01, Duration, Convexity, VaR, and Stress Tests are used to measure interest rate risk; how interest rate forwards, futures, and swaps are used to manage interest rate risk.

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  • We resolve these issues as follows. We show that a nonincreasing returns to scale (nrs) model is usually appropriate when modeling rational choice among investors. We show when multiple risk and return measures can justifiably be combined and identify some suitable measures. We show we need a nonlinear model to justify the assumption of convexity and to model diversification. We develop a method to approximate a solution to this model as accurately as needed using a sequence of linear models. Coherent measures of risk come up again and again in our discussion.

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