Spring 2011 Midterm 2 Formulas - MATH 472/567: Actuarial...

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Unformatted text preview: MATH 472/567: Actuarial Theory II/Topics in Actuarial Theory I Midterm #2: Formula Summary This review sheet contains the key concepts from Chapter 10 (10.1-10.3, 10.5-10.6), Chapter 11 (11.1-11.3), and Chapter 15 (15.1-15.2, 15.4, 15.6) of the text. Multiple Decrement Models : μ ( τ ) x ( t ) = ∑ m k =1 μ ( j ) x ( t ) t p ( τ ) x = exp [- R t μ ( τ ) x ( s ) ds ] t q ( τ ) x = 1 - t p ( τ ) x joint pdf of J and T: f T,J ( t, j ) = t p ( τ ) x μ ( j ) x ( t ) t q ( j ) x = R t f T,J ( s, j ) ds t q ( τ ) x = ∑ m k =1 t q ( j ) x marginal pmf of J: f J ( j ) = ∞ q ( j ) x marginal pdf of T: f T ( t ) = t p ( τ ) x μ ( τ ) x ( t ) f T,J ( t, j ) = f T | J ( t | j ) f J ( j ) = f J | T ( j | t ) f T ( t ) joint pmf of K and J: k | q ( j ) x = R k +1 k t p ( τ ) x μ ( j ) x ( t ) dt = k p ( τ ) x q ( j ) x + k l ( τ ) x + n = l ( τ ) x n p ( τ ) x n d ( τ ) x = l ( τ ) x n q ( τ ) x = l ( τ ) x- l ( τ ) x + n n d ( j ) x = l ( τ ) x n q ( j ) x n d ( τ ) x...
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This note was uploaded on 02/29/2012 for the course MATH 472 taught by Professor Zhu during the Spring '08 term at University of Illinois, Urbana Champaign.

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Spring 2011 Midterm 2 Formulas - MATH 472/567: Actuarial...

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