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Neuro-dynamic programming is a methodology for sequential decision making under uncertainty, which is based on dynamic programming. The key idea is to use a scoring function to select decisions in complex dynamic systems, arising in a broad variety of applications from engineering design, operations research, resource allocation, finance, etc. This is much like what is done in computer chess, where positions are evaluated by means of a scoring function and the move that leads to the position with the best score is chosen. Neuro-dynamic programming provides a class of systematic methods for computing appropriate scoring functions using approximation schemes and simulation/evaluation of the system’s performance.

In late June 2004, the Basel Committee on Banking Supervision approved and published a document entitled “International Convergence of Capital Measurement and Capital Standards: A revised Framework”, better known as the “Basel II framework”. The publication of this document marked the final milestone of a process that was over five years in the making. The fundamental improvements over the Basel I Accord of 1988 help explain this relatively long time span. The main objectives of the new framework, stated by the Basel Committee in its June 1999 Consultative Paper, were the following: To promote safety and soundness in the financial system. To enhance competitive equality. To adopt a more comprehensive approach to addressing risks. To continue to focus on internationally active banks, although the new framework’s principles should also be applicable to banks of varying levels of complexity and sophistication. Whereas the first two goals pick up where the Basel I Accord left off, the last two represent important advancements. The desire to develop a more comprehensive approach was a direct consequence of recognizing that the current regime lacks risk sensitivity in its minimum capital requirements and encourages market participants to exploit mechanisms of regulatory capital arbitrage.

Both under Solvency 2 and Basel II, operational risk is an important risk category for which the financial industry has to come up with a capital charge. Under Basel II, Operational Risk is defined as the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. This definition includes legal risk, but excludes strategic and reputational risk. In this talk I will discuss some of the issues underlying the quantitative modelling of operational risk.

This presentation has two purposes: (1) show operations researchers how they can apply quadratic binary programming to current problems in molecular biology, and (2) show formulations of some combinatorial optimization problems as integer programs. The former purpose is primary, and I wish to persuade researchers to enter this exciting frontier. The latter purpose is part of a work in progress.

Since 90s power markets are being restructured worldwide and nowadays electrical energy is traded as a commodity. Therewith the question how to manage and hedge the financial risks resulting from uncertain electrical power and fuel prices is essential for market participants. There exists a rich literature on risk management in energy markets. Some noteworthy references can be downloaded from our web resources [1] and are reviewed in the cited literature. Let us first investigate the market structure and then discuss two different pricing schemes for risk management in power industries.

Consider a general taxation model involving two levels of decision-making. The upper level (leader) imposes taxes on a specified set of goods or services while the lower level (follower) optimizes its own objective function, taking into account the taxation scheme devised by the leader. This model belongs to the class of bilevel optimization problems where both objective fucntions are bilinear.

Reliable implementation of geometric algorithms is a notoriously difficult task. Algorithms are usually designed for the Real-RAM, capable of computing with real numbers in the sense of mathematics, and for non-degenerate inputs. But, real computers are not Real-RAMs and inputs are frequently degenerate.

Many financial decision problems are most naturally formulated as optimization problems. This is the case, for example, in (arbitrage, utility, risk measure,...) pricing and hedging of (European, American, real,..) options, portfolio optimization and asset liability management. The optimization approach becomes even more natural in the presence of market imperfections such as transaction costs or portfolio constraints, where more traditional approaches of mathematical finance fail. Common to many financial problems, when properly formulated, is convexity with respect to the decision variables. This opens up possibilities of using numerical techniques that have been developed for large scale optimization problems.

A common issue for firms is how to allocate capital resources to various investment alternatives. An extensive literature in finance has examined various aspects of capital budgeting, including capital constraints, the determination of discount rates, and alternative approaches to estimating cash flows and handling risk, such as real options techniques. In terms of organizational structure, a central feature of the capital budgeting process in large firms is that relevant information about the profitability of potential investment projects resides with one or several managers. It is generally accepted that preferences of these managers may not coincide with those of the firm’s owners (the principal). Consequences of asymmetric information include strategic reporting by better-informed managers (for example, “sandbagging” or “creative optimism”) and a need to measure performance ex post . Surveys consistently find that internal rate of return (IRR) criteria remain prevalent in capital budgeting decisions. Furthermore the use of artificially high hurdle rates suggests widespread capital rationing [15, 20].

In the classical Vehicle Routing Problem (VRP) a fleet of capacitated vehicles is available to serve a set of customers with known demand. Each customer is required to be visited by exactly one vehicle and the objective is to minimize the total distance traveled. In the Split Delivery Vehicle Routing Problem (SDVRP) the restriction that each customer has to be visited exactly once is removed, i.e., split deliveries are allowed. In this paper we present a survey of the state-of-the-art on this important problem.