Part-2-331-2011-F

Part-2-331-2011-F - Review Notes ACTSC 331, FALL 2011 Part...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Review Notes ACTSC 331, FALL 2011 Part 2 Multiple State Models 1. Description of a Multiple State Model (MSM) : Assume that, at any time t , a life aged x has n + 1 states such as alive, dead, employed, unemployed, healthy, sick, disabled, and so on. The n + 1 states are labelled 0 , 1 ,...,n . For any time t , let Y ( t ) denote the states of ( x ) at time t , namely event ( Y ( t ) = i ) means the life is in state i at age x + t . Thus, for a given t 0, Y ( t ) is a discrete random variable with n + 1 possible values. In addition, the set of the random variables { Y ( t ) } t is a continuous-time stochastic process. 2. Assumptions and notation on a multiple state model. Assumption 1 (Markov property): For any states i and j and any t 0 and s 0, the conditional probability Pr { Y ( t + s ) = j | Y ( t ) = i } depends only on any information at the current time t and does not depend on any information before time t . Assumption 2: For any t 0 and h > 0, Pr { 2 or more transitions in the time period ( t, t + h ] } = o ( h ) . A function g ( h ) = o ( h ) means lim h g ( h ) h = 0 . Thus, if g i ( h ) = o ( h ) for i = 1 ,...,k , then k i =1 g i ( h ) = o ( h ), Q k i =1 g i ( h ) = o ( h ), and g i ( h ) = o ( h ), where is an arbitrary constant. Notation: For any states i and j and any x 0 and t 0, we define t p ij x = Pr { Y ( x + t ) = j | Y ( x ) = i } , t p ii x = Pr { Y ( x + s ) = i for all s [0 ,t ] | Y ( x ) = i } ....
View Full Document

Page1 / 5

Part-2-331-2011-F - Review Notes ACTSC 331, FALL 2011 Part...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online