Exponential tilting

Exponential Tilting (ET), Exponential Twisting, or Exponential Change of Measure (ECM) is a distribution shifting technique used in many parts of mathematics.
The different exponential tiltings of a random variable 
 
 
 
 X
 
 
 {\displaystyle X}
 
 is known as the <a href="/facts/Natural_exponential_family/KC9p8EDr">natural exponential family</a> of 
 
 
 
 X
 
 
 {\displaystyle X}
 
.
Exponential Tilting is used in <a href="/facts/Monte_Carlo_method/AkHjY7jc">Monte Carlo Estimation</a> for rare-event simulation, and <a href="/facts/Rejection_sampling/6kj9Bahq">rejection</a> and <a href="/facts/Importance_sampling/jrbUnMXa">importance sampling</a> in particular.
In mathematical finance Exponential Tilting is also known as Esscher tilting (or the <a href="/facts/Esscher_transform/Uhy9mKgy">Esscher transform</a>), and often combined with indirect <a href="/facts/Edgeworth_series/WJHXQ3JN">Edgeworth approximation</a> and is used in such contexts as insurance futures pricing.
The earliest formalization of Exponential Tilting is often attributed to Esscher with its use in importance sampling being attributed to <a href="/facts/David_Siegmund/3yAWbr8j">David Siegmund</a>.

Exponential tilting open-in-new

Exponential tilting