Actuarial Mathematics
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Actuarial Mathematics 2
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Discount function (definition) - answer-A positive valued function v, of two nonnegative variables, which satisfy the following relationship: v(s,t)v(t,u) = v(s,u) for all s, t, u. Other desirable features: v(s,s) = 1 for all s: v(s,t)v(t,s) = v(s,s) = 1 -> v(s,t) = v(t,s)^-1. For simplicities sake: v(0,t) = v(t). v(s,t) = v(t)/v(s). Definition: The rate of interest for the time interval k to k+1 is the quantity: - answer-i_k = v(k+1, k) - 1 Note: an investment of 1 unit at ...
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Actuarial Mathematics•Actuarial Mathematics
Two approaches to the concept of probability will be introduced later in the book: Classical probability and experimental probability. The former approach is developed using the foundation of set theory, and a quick review of the theory is in order. Readers familiar with the basics of set theory such as set builder notation, Venn diagrams, and the basic operations on sets, (unions, intersections, and complements) can skip this chapter. Set is the most basic term in mathematics. Some synony...
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Actuarial Mathematics•Actuarial Mathematics