Projects scheduling by the project portfolio selection, something that has its own complexity and its flexibility, can create different composition of the project portfolio. An integer programming model is formulated for the project portfolio selection and scheduling.Two heuristic algorithms, genetic algorithm (GA) and simulated annealing (SA), are presented to solve the problem. Results of cal...

This entry provides a brief overview of credit migration or transition matrices, which characterize past changes in credit quality of obligors (typically firms). They are cardinal inputs to many risk management applications, including portfolio risk assessment, the pricing of bonds and credit derivatives, and the assessment of regulatory capital as is the case for the New Basel Accord. I addres...

We propose two new methods for attributing the risk of a portfolio or system to its components, when it is required to produce non-negative risk components that sum to the risk of the portfolio or system as a whole. One method attributes risk entirely to losses, taking profits for granted. The other method does allow profits in some scenarios to offset losses in other scenarios to some extent, ...

In the context of multi-period stock market investment with options, we provide characterization of the wealth of constantly rebalanced portfolios of stocks and options. This characterization takes advantage of a correspondence between certain combinations of options and pure gambling opportunities. Through this equivalence, prices to be set for the options correspond to payoff odds on the gamb...

Software product line engineering aims to reduce development time, effort, cost, and complexity by taking advantage of the commonality within a portfolio of similar products. The effectiveness of a software product line approach directly depends on how well feature variability within the portfolio is implemented and managed throughout the development lifecycle, from early analysis through maint...

The notion of drawdown is central to active portfolio management. Conditional Drawdown-at-Risk (CDaR) is defined as the average of a specified percentage of the largest drawdowns over an investment horizon and includes maximum and average drawdowns as particular cases. The necessary optimality conditions for a portfolio optimization problem with CDaR yield the capital asset pricing model (CAPM)...

Modern portfolio theory(MPT) addresses the problem of determining the optimum allocation of investment resources among a set of candidate assets. In the original mean-variance approach of Markowitz, volatility is taken as a proxy for risk, conflating uncertainty with risk. There have been many subsequent attempts to alleviate that weakness which, typically, combine utility and risk. We present ...

We review recent results on the new concept of worst-case portfolio optimization, i.e. we consider the determination of portfolio processes which yield the highest worst-case expected utility bound if the stock price may have uncertain (down) jumps. The optimal portfolios are derived as solutions of non-linear differential equations which itself are consequences of a Bellman principle for worst...

Patent application numbers grow exponentially in many industries, a phenomenon that has been linked to high fragmentation of patent ownership. Contradicting these findings and theoretical arguments, we show that such fragmentation is not a precondition for sudden and strong increases in patenting. We describe and analyze a patent portfolio race in an industry with highly concentrated patent own...

We propose a method for extending a given asset pricing formula to account for two additional sources of risk: the risk associated with future changes in market–calibrated parameters and the remaining risk associated with idiosyncratic variations in the individual assets described by the formula. The paper makes simple and natural assumptions for how these risks behave. These extra risks should...