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May 2011

Pedagogical Research Lecture
February 2011

Prof. Karl Sigman, Professor of Department of Industrial Engineering and Operations Research at Columbia University, was invited to speak at RMI's Pedagogical Research Lecture held on 10 February 2011.

Prof. Sigman spoke on the Introduction to Monte Carlo Simulation with Applications. He gave an overview of Monte Carlo simulation methods for use in estimating quantities of interest in various fields within the engineering and mathematical sciences.

Starting with the basics of generating random numbers with a given distributions, Prof. Sigman then reviewed how the strong law of large numbers and the central limit theorem from probability theory rigorously justify the precision of our estimates through confidence intervals. Examples were given for estimating difficult to compute multi- dimensional integrals, prices of complex stock options, ruin probabilities, waiting time distributions in complex queueing models, and even estimating the number of ways there can be a tie in a U.S. Presidential election. Some more advanced techniques, such as Markov Chain Monte Carlo (MCMC) and exact simulation, were also discussed.

RMI Workshop Series
February - April 2011

In February, Prof. Sanjiv Das from Santa Clara University and Prof. Robert Elliott of University of Calgary presented at research workshop organized by RMI which were attended by NUS faculty and students. Prof. Sanjiv took the first session and spoke on two topics: 1. The Principal Principle: Optimal Modification of Distressed Home Loans and 2. Strategic Loan Modification: An Options- Based Response to Strategic Default. Prof. Elliott continued with the second half of the research workshop series and presented his research paper entitled 'Hidden Markov Models, Altman Z-scores and Credit Ratings'. Credit ratings and accounting-based Altman Z-scores are two important sources of information for assessing the creditworthiness, or likelihood of defaults, of firms. In his paper, Prof. Elliott built a flexible, quantitative model based on a double Hidden Markov Model (DHMM) to extract information about the "true" credit qualities of firms from both the Z-scores evaluated from the accounting ratios of the firms and publicly available credit ratings of the firms produced by rating agencies.

RMI's monthly Research Workshop Series on 4 March welcomed two speakers: Prof. Frank Milne of Queen's University and Prof. Takao Kobayashi from the University of Tokyo. Prof. Frank Milne presented his paper on the general approaches for modeling liquidity effects in asset markets and their application to risk management systems, while Prof. Kobayashi spoke on the human capital as age-dependent asset mix and optimal life cycle portfolios. Prof. Kobayashi presented a theoretical model showing the effect of investors' age on their optimal portfolio characteristics in the context of Japanese economy where seniority based on age plays an important role in the determination of one's salary.

On 1 April, Prof. Kim Baeho from the Korea University Business School and Prof. Li Junye from ESSEC Business School were invited to speak at an RMI's Research Workshop Series. Prof. Kim started the workshop by presenting his paper on "Systemic Risk: What Defaults Are Telling Us", which developed dynamic measures of the systemic risk of the financial sector as a whole that defined systemic risk as the conditional probability of failure of a sufficiently large fraction of the total population of financial institutions. Separately, Prof. Li Junye presented his research paper which proposed a simulation-based parameter learning method. Prof. Li also presented an application of his proposed algorithm applied to real world financial data in the estimation of the Heston stochastic volatility model and Merton's structural credit risk model.

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Published quarterly by Risk Management Institute, NUS
Editor: Ivy Wang (rmiwy@nus.edu.sg)