The main objective of this thesis is to develop novel Monte Carlo techniques with emphasis on various applications in finance and economics, particularly in the fields of risk management and asset returns modeling. New stochastic algorithms are developed for rare-event probability estimation,...

We present a novel method, called the transform likelihood ratio (TLR) method, for estimation of rare event probabilities with heavy-tailed distributions. Via a simple transformation ( change of variables) technique the TLR method reduces the original rare event probability estimation with heavy...

We consider the problem of efficient estimation of tail probabilities of sums of correlated lognormals via simulation. This problem is motivated by the tail analysis of portfolios of assets driven by correlated Black-Scholes models. We propose two estimators that can be rigorously shown to be...

In this work we develop a methodology to reduce the variance when applying Monte Carlo simulation to the pricing of a European, American or Barrier option in a stochastic volatility environment. We begin by presenting some applicable concepts in the theory of stochastic differential equations....