P.hd in Computational Mathematics

P.hd in Computational Mathematics

Our research focuses on applied probability issues in areas including financial and insurance mathematics, performance analysis and optimization, communications networks and e-commerce. One important thrust area involves development of probabilistic asymptotes and efficient Monte Carlo simulation methodologies for small but important probabilities. These include applications in finance such as measuring and controlling probability of large losses due to credit risk in a loan portfolio, due to market risk in an investment portfolio. In insurance settings we consider estimation of ruin probabilities. In networks this involves estimation of extremely small buffer overflow and large delay probabilities. In reliability systems this involves estimation of performance measures such as system unreliability and mean time to failure. Other areas of interest include developing efficient simulation methodologies to price complex financial options, simulation based ordinal optimization methodologies, computational issues in Internet auctions. From methodological point of view, we focus primarily on simulation theory, queuing theory, large deviations theory and stochastic optimization.