Portfolio insurance allows investors to recover, at maturity, a given percentage of their initial capital. This limits downside risk in falling markets. Besides, it allows some participation in rising markets. One of the standard portfolio insurance methods is the Constant Proportion Portfolio Insurance (CPPI). We analyse options on cushion associated to CPPI. This kind of Power options corresp...

Mean-variance portfolio analysis provided the first quantitative treatment of the tradeoff between profit and risk. We describe in detail the interplay between objective and constraints in a number of single-period variants, including semivariance models. Particular emphasis is laid on avoiding the penalization of overperformance. The results are then used as building blocks in the development ...

Modern Portfolio Theory (MPT) is based upon the classical Markowitz model which uses variance as a risk measure. A generalisation of this approach leads to mean-risk models, in which a return distribution is characterised by the expected value of return (desired to be large) and a ”risk” value (desired to be kept small). Portfolio choice is made by solving an optimisation problem, in which the ...

The main business of banks and insurance companies is risk. Banks and financial institutions lend money, running the risk of losing the lended amount, and they borrow “short money” having less risk but higher expected rates of return. Insurance companies on the other hand earn a risk premium for guaranteeing indemnifification for a negative outcome of a certain event. The evaluation of risk is ...

The European Union carbon market is undergoing rapid development and its interdependence with fossil fuel markets is increasingly important for energy investors. In this study, exponential general autoregressive conditional heteroskedastic models, extreme value theory and copulas are used to evaluate downside risk through the traditional value-at-risk and expected shortfall measurements. Empiri...

We present a new approach that enables investors to seek a reasonably robust policy for portfolio selection in the presence of rare but high-impact realization of moment uncertainty. In practice, portfolio managers face diffculty in seeking a balance between relying on their knowledge of a reference financial model and taking into account possible ambiguity of the model. Based on the concept of...