Sandeep Juneja

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Consider the problem of estimating the small probability that the maximum of a random walk exceeds a large threshold, when the process has a negative drift and the underlying random variables may have heavy tailed distributions. We consider one class of such problems that has applications in estimating the ruin probability associated with insurance claim(More)
We consider the risk of a portfolio comprising loans, bonds, and financial instruments that are subject to possible default. In particular, we are interested in performance measures such as the probability that the portfolio incurs large losses over a fixed time horizon, and the expected excess loss given that large losses are incurred during this horizon.(More)
We consider the problem of optimal allocation of computing budget to maximize the probability of correct selection in the ordinal optimization setting. This problem has been studied in the literature in an approximate mathematical framework under the assumption that the underlying random variables have a Gaussian distribution. We use the large deviations(More)
Risk measurement for derivative portfolios almost invariably calls for nested simulation. In the outer step one draws realizations of all risk factors up to the horizon, and in the inner step one re-prices each instrument in the portfolio at the horizon conditional on the drawn risk factors. Practitioners may perceive the computational burden of such nested(More)
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 efficient as the tail probability of interest decreases to zero.(More)
<lb>We consider the non-cooperative choice of arrival times by individual users, who<lb>seek service at a first-come first-served queueing system that opens up at a given time.<lb>Each user wishes to obtain service as early as possible, while minimizing the expected<lb>wait in the queue. This problem was recently studied within a simplified(More)
In this introductory tutorial we discuss the problem of pricing financial derivatives, the key application of Monte Carlo in finance. We review the mathematics that uses no-arbitrage principle to price derivatives and expresses derivatives price as an expectation under the equivalent martingale measure. In the presentation at the conference we will also(More)