### Real Options:

Real options valuation, also often termed real options analysis, applies option valuation techniques to capital budgeting decisions. A real option itself, is the right -- but not the obligation -- to undertake certain business initiatives, such as deferring, abandoning, expanding, staging, or contracting a capital investment project. For example, the opportunity to invest in the expansion of a firm's factory, or alternatively to sell the factory, is a real call or put option, respectively. Real options are generally distinguished from conventional financial options in that they are not typically traded as securities, and do not usually involve decisions on an underlying asset that is traded as a financial security.

### Revenue Management:

By Revenue Management (RM), we mean the process of understanding, forecasting and influencing consumer behaviour in order to maximise a firm's revenues. Put simply, RM is all about selling the right product to the right customer at the right time for the right price. RM originated in the airline industry under the term Yield Management. Today, RM is widely employed in many other major industries, such as hotels, restaurants, car rentals and carparks. A prospective research student in this area should expect to gain knowledge on Optimisation, Markov Processes, Dynamic programming and HJB equations.

### Optimal Queues:

Queuing theory was first derived in the beginnings of the 20th century and was applied in tele-traffic engineering. Queueing theory can be used to analyse and model service providing systems under stochastic demands. Applications cover a wide field such as customer service, response centres, communications and public transformations. We are principally interested in modelling the value of a managerial decision (like a Real Option) given some financial payoff depending on a queue. One such example is balancing the cost of employing servers against penalties on missed customers, resulting in a crossover to the subjects of Dynamic programming, Optimisation and Markov Processes.

### Cash Holdings, Debt and Investment Decisions:

We propose a framework for evaluating investment decisions given the current (and future expected) levels of liquid assets held by the firm. At its most simplistic level we can describe a situation where a classic real option over estimates the value of an option by assuming that the firm has sufficient liquid assets to cover short term losses. We are looking to extend this framework into more complex, dynamic systems such as modelling the optimal cash reserve held at a commercial bank. Future work here could touch on Game theory, Economics, Dynamic programming and HJB equations.

### Optimization of Storage in Power Systems:

Our interests are in models for combined physical and economical systems which have uncertain price, uncertain physical flows and deterministic dynamics, including variables that are stored or integrated which can be described by a single PDE equation. Examples are the optimal storage and smoothing of wind power, the optimal timing of electrical heating or cooling, or investment in power generators. Research in this area could include Optimisation, numerical techniques for PDEs, Dynamic programming and HJB equations.