Importance sampling of compounding processes

Abstract

Compounding processes, also known as perpetuities, play an important role in many applications; in particular, in time series analysis and mathematical finance. Apart from some special cases, the distribution of a perpetuity is hard to compute, and large deviations estimates sometimes involve complicated constants which depend on the complete distribution. Motivated by this, we propose provably efficient importance sampling algorithms which apply to qualitatively different cases, leading to light and heavy tails. Both algorithms have the non-standard feature of being statedependent. In addition, in order to verify the efficiency, we apply recently developed techniques based on Lyapunov inequalities.

Importance sampling of heavy-tailed iterated random functions

“…Asmussen and Nielsen [3] also studied rare-event simulation for perpetuities and iterated random functions considering deterministic interest rates. Blanchet and Zwart [7] estimated the tail probability of perpetuities with deterministic premiums (B n ). Later, Blanchet et al [6] developed simulation algorithms Importance sampling of heavy-tailed iterated random functions 807 for perpetuities when the discount factor and premium are modeled by a Markov chain.…”

Efficient rare event simulation of continuous time Markovian perpetuities

“…rewards and discounts (see, for instance, Devroye, Fill, and Neininger (2000) and Devroye, and Neininger, (2002)). Rare event simulation for perpetuities, on the other hand has been studied in Asmussen and Nielsen (1995) in the context of deterministic interest rates and Blanchet and Zwart (2007) in some discrete settings involving i.i.d. discount rates.…”