Narrow Results

An example about non-convergence of Perron–Bremermann envelopes on the unit ball in Cⁿ is constructed. Under additional conditions, we show that convergence of envelopes is possible. We also deal with a representation of envelope in the style of Poletsky on domains which are not necessarily strictly pseudoconvex.

We show that in ℂ² if the set of strongly regular points are closed in the boundary of a smooth bounded pseudoconvex domain, then the domain is c-regular, that is, the plurisubharmonic upper envelopes of functions continuous up to the boundary are continuous on the closure of the domain. Using this result we prove that smooth bounded pseudoconvex Reinhardt domains in ℂ² are c-regular.

In this chapter, we look at how estimation is performed on an important finance valuation model to address the problem of risk pricing and also to apply the model to evaluate investment performances.

A key foundation of finance is the tradeoff between risk and return. Assets returning higher ex-ante (or conditional expected) return should also bear higher ex-ante risk, and vice versa. Finance theory and models seek to establish the exact relationship between this return and risk. One of the earliest finance models is the Sharpe-Lintner capital asset pricing model (CAPM) that links expected return to only systematic risk. The unsystematic or residual risk can be diversified away and is, therefore, not priced. Systematic risk in the form of market risk is priced. For any asset, this market risk is reflected in the sensitivity of the asset return to the market factor movement. Higher sensitivity implies a higher beta or systematic risk. When we refer to risk, it is usually quantified in terms of standard deviation instead of variance since the former is expressed in terms of the same unit as the underlying variable. We shall begin our study of CAPM with the statistical market model.