Mark Broadie

Efficient Risk Estimation via Nested Sequential Simulation

Management Science · 2011-04-30 · 119 citations

We analyze the computational problem of estimating financial risk in a nested simulation. In this approach, an outer simulation is used to generate financial scenarios, and an inner simulation is used to estimate future portfolio values in each scenario. We focus on one risk measure, the probability of a large loss, and we propose a new algorithm to estimate this risk. Our algorithm sequentially allocates computational effort in the inner simulation based on marginal changes in the risk estimato…

General Bounds and Finite-Time Improvement for the Kiefer-Wolfowitz Stochastic Approximation Algorithm

Operations Research · 2011-10-01 · 101 citations

We consider the Kiefer-Wolfowitz (KW) stochastic approximation algorithm and derive general upper bounds on its mean-squared error. The bounds are established using an elementary induction argument and phrased directly in the terms of tuning sequences of the algorithm. From this we deduce the nonnecessity of one of the main assumptions imposed on the tuning sequences by Kiefer and Wolfowitz [Kiefer, J., J. Wolfowitz. 1952. Stochastic estimation of the maximum of a regression function. Ann. Math.…

Risk Estimation via Regression

Operations Research · 2015-10-01 · 98 citations

We introduce a regression-based nested Monte Carlo simulation method for the estimation of financial risk. An outer simulation level is used to generate financial risk factors and an inner simulation level is used to price securities and compute portfolio losses given risk factor outcomes. The mean squared error (MSE) of standard nested simulation converges at the rate k −2/3 , where k measures computational effort. The proposed regression method combines information from different risk factor r…

Assessing Golfer Performance on the PGA TOUR

INFORMS Journal on Applied Analytics · 2012-04-01 · 71 citations

The game of golf involves many different types of shots, including long tee shots (typically hit with a driver), approach shots to greens, shots from the sand, and putts on the green. Although determining the winner of a golf tournament by counting strokes is easy, assessing which factors contributed most to the victory is not. In this paper, we apply an analysis based on strokes gained, introduced previously, to assess professional golfer performance in different parts of the game [Broadie M (2…

Every Shot Counts: Using the Revolutionary Strokes Gained Approach to Improve Your Golf Performance and Strategy

Medical Entomology and Zoology · 2014-03-06 · 44 citations