Showing papers by "L. Jeff Hong published in 2010"

Pathwise Estimation of Probability Sensitivities Through Terminating or Steady-State Simulations

Abstract: A probability is the expectation of an indicator function. However, the standard pathwise sensitivity estimation approach, which interchanges the differentiation and expectation, cannot be directly applied because the indicator function is discontinuous. In this paper, we design a pathwise sensitivity estimator for probability functions based on a result of Hong [Hong, L. J. 2009. Estimating quantile sensitivities. Oper. Res.57(1) 118--130]. We show that the estimator is consistent and follows a central limit theorem for simulation outputs from both terminating and steady-state simulations, and the optimal rate of convergence of the estimator is n-2/5 where n is the sample size. We further demonstrate how to use importance sampling to accelerate the rate of convergence of the estimator to n-1/2, which is the typical rate of convergence for statistical estimation. We illustrate the performances of our estimators and compare them to other well-known estimators through several examples.

Robust simulation of environmental policies using the DICE model

Abstract: Integrated assessment models that combine geophysics and economics features are often used to evaluate environmental economic policies. In these models, there are often profound uncertainties and Monte Carlo simulations are often used to evaluate the policies. Generally, the simulation approach requires that the distribution of the uncertain parameters are clearly specified. In this paper, we adopt the widely used multivariate normal distribution to model the uncertain parameters. However, we assume that the mean vector and covariance matrix of the distribution are within some ambiguity sets. We propose a change-of-measure technique to derive the simulation results for any mean vector and covariance matrix in the sets without actually simulating them. We then show how to find the worst case performance for all mean vectors and covariance matrices in the ambiguity sets by solving a sequence of convex problems. This performance provides a robust evaluation of the policies. We test our algorithm on a famous environmental economic model, known as the DICE model, and obtain some insightful and interesting results.

Fighting Strategies in a Market with Counterfeits

Abstract: Counterfeiting is a widely spread phenomenon and has seen rapid growth in recent years. In this paper, we adopt the standard vertical differentiation model and allow consumers the choices of purchasing an authentic product, purchasing a counterfeit, or not buying. We focus on how non-deceptive counterfeits, which consumers know at time of purchase that the products are counterfeits with certainty, affect the price, market share and profitability of brand name products. We also consider the strategies for brand name companies to fight counterfeiting. We compare different fighting strategies in a market with one brand name product and its counterfeit, and derive equilibrium fighting strategies in a market with two competing brand name products and a counterfeit under general conditions.