Abstract Many pricing problems boil down to the computation of a high-dimensional integral, which is usually estimated using Monte Carlo. In fact, accuracy Carlo estimator with M simulations given by σ M {\frac{\sigma}{\sqrt{M}}} . Meaning that its convergence immu...

This paper is concerned with the efficient simulation of P (Sn > s) where Sn is the sum of n i.i.d. heavy-tailed random variables X1, . . . ,Xn. Asmussen and Kroese (2006) and Asmussen and Kortschak (2012) proposed estimators that combine exchangeability arguments with conditional Monte-Carlo and whose relative errors go to 0 as s→∞. We useMn = max (X1, . . . ,Xn) as a control variate to propos...

We present and analyze an algorithm to solve numerically BSDEs based on Picard’s iterations and on a sequential control variate technique. Its convergence is geometric. Moreover, the solution provided by our algorithm is regular both w.r.t. time and space.

In this paper we present a strategy to form a class of control variates for pricing Asian options under the stochastic volatility models by the risk-neutral pricing formula. Our idea is employing a deterministic volatility function σ(t) to replace the stochastic volatility σt. Under the Hull and White model[11] and the Heston model[10], the deterministic volatility function σ(t) can be chosen w...

Monte Carlo simulation is widely used in many fields. Unfortunately, it usually requires a large amount of computer time to obtain even moderate precision so it is necessary to apply efficiency improvement techniques. Adaptive Monte Carlo methods are specialized Monte Carlo simulation techniques where the methods are adaptively tuned as the simulation progresses. The primary focus of such techn...

It is well known that Markov chain Monte Carlo (MCMC) methods scale poorly with dataset size. We compare the performance of two classes of methods which aim to solve this issue: stochastic gradient MCMC (SGMCMC), and divide and conquer methods. We find an SGMCMC method, stochastic gradient Langevin dynamics (SGLD) to be the most robust in these comparisons. This method makes use of a noisy esti...

Policy gradient methods have achieved remarkable successes in solving challenging reinforcement learning problems. However, it still often suffers from the large variance issue on policy gradient estimation, which leads to poor sample efficiency during training. In this work, we propose a control variate method to effectively reduce variance for policy gradient methods. Motivated by the Stein’s...

In this paper we present a simple control variate method, for options pricing under stochastic volatility models by the risk-neutral pricing formula, which is based on the order moment of the stochastic factor Yt of the stochastic volatility for choosing a non-random factor Y (t) with the same order moment. We construct the control variate using a stochastic differential equation with a determi...

Adaptive Monte Carlo methods are simulation efficiency improvement techniques designed to adaptively tune simulation estimators. Most of the work on adaptive Monte Carlo methods has been devoted to adaptively tuning importance sampling schemes. We instead focus on adaptive methods based on control variate schemes. We introduce two adaptive control variate methods, and develop their asymptotic p...