Abstract: This talk reviews the basic ideas of quantitative investment in layman terms. No previous knowledge about finance is assumed. We review the estimation of the st atistics of returns on investment, and the Markowitz-Sharpe portfolio theory. We also discuss the rudiments of the Black-Scholes option pricing formula, includi ng the concepts of Delta and dynamic hedging. Finally, we focus the discussion o n the notion of 'convexity trading', whereby agents transact in volatility but keep, at the same time, a market-neutral position. The idea of investment in volatility, as opposed to investing in a portfolio of stocks, is considered as an alternative form of investment that may be suitable in highly v olatile markets. The talk concludes with a set of recommended readings and open problems.

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Abstract: One of the principal goals of quantitative analysts is to measure the exposure of financial assets to changes in the market environment. This is done by computing the sensitivities of the 'model price' with respect to perturbations in the prices of benchmark securities. We present a methodology for calculating these sensitivities in the context of Monte Carlo simulations. The results are applied for measuring the risk of complex financial instruments.

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Abstract: We review here the problem of specifying the parameters of a probability distribution used for pricing derivative securities and contingent claims. We consider, in particular, the problem of fitting a diffusion process so as to price correc tly a large set of option prices by taking expectations over the distribution. This is an ill-posed problem which requires techniques from inverse problems in PDEs, moment problems in probability, and other techniques.

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