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In 1952, Harry M. Markowitz published a seminal paper about analyzing portfolios. In 1990, he was awarded the Nobel Prize for his portfolio theory. Markowitz portfolio analysis delineates a set of highly desirable investment portfolios. These optimal portfolios have the maximum return at each plausible level of risk, computed iteratively over a range of different risk levels. Conversely, Markowitz portfolio analysis can find the same set of optimal investments by delineating portfolios that have the minimum risk over a range of different rates of return. The set of all Markowitz optimal portfolios is called the efficient frontier. Portfolio analysis analyzes rate of return statistics, risk statistics (standard deviations), and correlations from a list of candidate investments (stocks, bonds, and so on) to determine which investments, and in what proportions (weights), enter into every efficient portfolio. Further analysis of Markowitz΄s portfolio theory reveals interesting asset pricing implications. [ABSTRACT FROM AUTHOR]

This chapter considers the setting of the appropriate level of insurance in a broader context of business decisions, concerning also risk transfer through reinsurance, and the rate of return on capital required to ensure solvability. An approach based on the distribution of the single year loss and the basic problem of joint decisions on premiums and capital needed to ensure safety in terms of shareholder's choice of the level of expected rate of return and risk, are presented. This chapter also presents in more details the problem of decomposition of the whole-portfolio premium into individual risk premiums. The problem extended by allowing for reinsurance, where competitiveness is a result of simultaneous choice of the amount of capital and retention level is also discussed.

Modeling speech signals in the short-time Fourier transform (STFT) domain is a fundamental problem in designing speech enhancement systems. This chapter introduces a novel modeling approach, which is based on generalized autoregressive conditional heteroscedasticity (GARCH). GARCH is widely-used for volatility modeling of financial time-series such as exchange rates and stock returns. GARCH models take into account the heavy tailed distribution and volatility clustering characteristics of financial time-series. Spectral analysis shows that speech signals in the STFT domain are also characterized by heavy tailed distributions and volatility clustering. We demonstrate the application of GARCH modeling to speech enhancement, and show its advantage compared to using the conventional decision-directed method. [ABSTRACT FROM AUTHOR]