Approximating Martingales for Variance Reduction
نویسندگان
چکیده
\Knowledge of either analytical or numerical approximations should enable more eecient simulation estima-tors to be constructed." This principle seems intuitively plausible and certainly attractive, yet no completely satisfactory general methodology has been developed to exploit it. We present a new approach for Markov processes that relies on the construction of a martingale that is strongly correlated with the performance measure of interest. As such, the method may be viewed as a special case of the internal control variates eeciency improvement technique.
منابع مشابه
Approximating Martingales for Variance Reduction in Markov Process Simulation
Knowledge of either analytical or numerical approximations should enable more efficient simulation estimators to be constructed.” This principle seems intuitively plausible and certainly attractive, yet no completely satisfactory general methodology has been developed to exploit it. We present a new approach for obtaining variance reduction in Markov process simulation that is applicable to a v...
متن کاملAsymmetric Variance Reduction for Pricing American Options
Based on the dual formulation by Rogers (2002), Monte Carlo algorithms to estimate the high-biased and low-biased estimates for American option prices are proposed. Bounds for pricing errors and the variance of biased estimators are shown to be dependent on hedging martingales. These martingales are applied to (1) simultaneously reduce the error bound and the variance of the high-biased estimat...
متن کاملMartingale Approximations for Sums of Stationary Processes
Approximations to sums of stationary and ergodic sequences by martingales are investigated. Necessary and sufficient conditions for such sums to be asymptotically normal conditionally given the past up to time 0 are obtained. It is first shown that a martingale approximation is necessary for such normality and then that the sums are asymptotically normal if and only if the approximating marting...
متن کاملOptimal stopping via path-wise dual empirical maximization
The optimal stopping problem arising in the pricing of American options can be tackled by the so called dual martingale approach. In this approach, a dual problem is formulated over the space of martingales. A feasible solution of the dual problem yields an upper bound for the solution of the original primal problem. In practice, the optimization is performed over a finite-dimensional subspace ...
متن کاملThe Structure of Bhattacharyya Matrix in Natural Exponential Family and Its Role in Approximating the Variance of a Statistics
In most situations the best estimator of a function of the parameter exists, but sometimes it has a complex form and we cannot compute its variance explicitly. Therefore, a lower bound for the variance of an estimator is one of the fundamentals in the estimation theory, because it gives us an idea about the accuracy of an estimator. It is well-known in statistical inference that the Cram&eac...
متن کامل