## 1 Introduction  
With the transition towards a low-carbon energy supply system underway, the share of electricity generated by renewable energy resources (RER) is likely to increase. In Europe, wind and solar energy have the highest potential in terms of renewable electricity generation [1]. Wind and solar energy resources are intermittent, as their availability depends on weather patterns [2]. To maintain the system frequency within acceptable limits, electricity supply and demand needs to be balanced. Traditionally, supply could be adjusted to match demand by dispatching fossil-fueled generators. Given the transition towards renewable energy generation, the traditional electricity grid needs to be shifted towards the so-called _smart grid_ notion, in which new technologies can be implemented without jeopardizing grid reliability and efficiency, and which make the grid less environmentally friendly [3]. A smart grid allows grid-elements which are only passively used in the current electricity system to become actively involved in the provision of system services such as balancing activities [4]. An important aspect of smart grids is Demand Response (DR). Also known as a category of the general term demand side management [5; 6], Demand response is defined by [7] as 'The process through which final consumers (households or businesses) provide flexibility to the electricity system by voluntarily changing their usual electricity consumption in reaction to price signals or to specific requests, while at the same time benefiting from doing so'. In the deregulated energy market, a consumer that takes an active role in energy generation and/or provision of flexibility services is referred to as a prosumer [8; 9]. For small consumers to become prosumers by using their flexible load for financial or balancing purposes, a new role is needed in the energy value chain: the role of aggregators. An aggregator is defined by [10] as 'an intermediary between small consumers and other players (e.g., the retailers, or distribution companies) in the system' (pp.138). Aggregators bundle the flexibility of individual consumers or businesses into a portfolio of devices that are either switched on or off, depending on grid stabilization requirements. In so doing, aggregators enable smaller system users (consumers or producers) to participate indirectly in the market through the provision of flexibility services, and to receive financial benefits in return. An example of this is Direct Load Control (DLC), in which the aggregator directly controls a set of appliances within the end-user's premises [11]. Recent developments in the energy market liberalization process have created several opportunities for aggregators for the provision of market-based products and services [12]. In the Netherlands, short-term frequency deviations are balanced through the Frequency Containment Reserve (FCR) market, also known as primary reserve [13]. In the FCR market, a bidding system is applied in which parties offer a certain amount of flexible power that they can deliver whenever necessary. In return, they receive financial compensation from the Transmission System Operator (TSO) for the capacity they have offered. Given that FCR is important to system reliability, it must be provided continuously, with an availability of 100% [14]. Not meeting the promised bid results in a fine, which the DR-aggregator must pay to the TSO. Aggregators need to construct their flexible portfolio of DR assets in such a way that it delivers the promised amount of flexibility while meeting the prerequisites of the FCR market. With a given portfolio, aggregators can choose how much flexibility they are willing to provide during the next bidding period. Determining the bid size for each bidding period is a strategic process. If the aggregator bids too low, revenue, and thus profit, can be suboptimal. On the other hand, if the aggregator bids too high, the aggregator might be unable to deliver the flexibility, and thus risks a fine.