Conditional Expectation and Change of Measure

2011 ◽  
pp. 107-122
Keyword(s):  
Conditional Expectation ◽  
Change Of Measure

Conditional Expectation and Change of Measure

2012 ◽  
Author(s):  
Svetlozar T. Rachev ◽  
Young Shin Kim ◽  
Michele Leonardo Bianchi ◽  
Frank J. Fabozzi
Keyword(s):  
Conditional Expectation ◽  
Change Of Measure

scholarly journals Computation of Compound Distributions I: Aliasing Errors and Exponential Tilting

1999 ◽  
Vol 29 (2) ◽  
pp. 197-214 ◽  
Author(s):  
Rudolf Grübel ◽  
Renate Hermesmeier
Keyword(s):  
Numerical Evaluation ◽  
Change Of Measure ◽  
Exponential Tilting ◽  
Transform Methods ◽  
Compound Distributions ◽  
Heavy Tailed Distributions ◽  
Panjer Recursion ◽  
Heavy Tailed ◽  
Suitable Change

AbstractNumerical evaluation of compound distributions is one of the central numerical tasks in insurance mathematics. Two widely used techniques are Panjer recursion and transform methods. Many authors have pointed out that aliasing errors imply the need to consider the whole distribution if transform methods are used, a potential drawback especially for heavy-tailed distributions. We investigate the magnitude of aliasing errors and show that this problem can be solved by a suitable change of measure.

scholarly journals Some conditional expectation identities for the multivariate normal

2010 ◽  
Vol 101 (9) ◽  
pp. 2250-2253 ◽  
Author(s):  
Christopher S. Withers ◽  
Saralees Nadarajah
Keyword(s):  
Conditional Expectation ◽  
Multivariate Normal

Expect the Unexpected from Conditional Expectation

1998 ◽  
Vol 52 (3) ◽  
pp. 248 ◽  
Author(s):  
Michael A. Proschan ◽  
Brett Presnell
Keyword(s):  
Conditional Expectation

Quadratic transformations: a model for population growth. II

1970 ◽  
Vol 2 (02) ◽  
pp. 179-228 ◽  
Author(s):  
Harry Kesten
Keyword(s):  
Population Growth ◽  
Convergence Theorem ◽  
Conditional Expectation ◽  
High Probability ◽  
Random Variables ◽  
Convergence Results ◽  
General Convergence

In this last part theFn(i) andMn(i) are considered as random variables whose distributions are described by the model and various mating rules of Section 2. Several convergence results will be proved for those specific mating rules, but we begin with the more general convergence theorem 6.1. The proof of this theorem brings out the basic idea of this section, namely that whenFnandMnare large,Fn + 1(i) andMn + 1(i) will, with high probability, be close to a certain function ofFn(·) andMn(·) (roughly the conditional expectation ofFn+1(i) andMn + 1(i) givenFn(·) andMn(·)).

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