This chapter examines political risk insurance as an alternative to international investment treaties, looking at some of the world’s leading providers of this service. It continues with a consideration of investment incentives, followed by a discussion of some of the main sources for further information on international investment law. This chapter then offers a concluding overview of some of the central debates in international investment law.

The dynamics of the EU legal order result from interactions between a great diversity of actors. The main characteristics of key actors explain the specific role attributed to each of them in the functioning of the EU, as will be further set out in subsequent chapters. The Member States, to start with, play a prominent and decisive role in shaping the nature and boundaries of the EU legal order (Section 2.1). Alongside this, nationals of the Member States are today an important part of the system of checks and balances, and are referred to as EU citizens (Section 2.2). Yet it is to the specific and sophisticated set of institutions (Section 2.3) and complementary organs (Section 2.4) that breathe life into the EU legal order that much of our attention in this chapter will be devoted.

We will study the pricing of European contingent claims within this model through determining the existence of a risk-neutral probability measure and replicating strategies. The results and computations in this chapter serve as motivation and preparation for the Black–Scholes model.

The main aim in this chapter is to introduce the Black–Scholes model and to study how this model is used to price financial options. Although, in reality, trading is done by computers and therefore stocks are traded at discrete times, the times between successive trades can be extremely short and therefore trading strategies can be well approximated by continuous-time processes. The advantage of this is that one can use the machinery of stochastic calculus to do computations which would potentially be very complicated if attempted directly using the discrete-time formulas from the first half of this book.

This chapter explores the controversial topic of dispute settlement under international investment law, considering the much-maligned investor–state dispute settlement and its reforms, including the EU’s investment court system and alternative dispute settlement mechanisms.

This chapter considers the two forms of non-discrimination found in most investment treaties: national treatment and most favoured nation, exploring the main legal controversies with these concepts including the need to establish like circumstances of the foreign investor as compared to a local investor or other foreign investor under a different treaty.

The binomial or Cox–Ross–Rubinstein (CRR) model is a simple discrete model for the financial market. The advantage of this model is that it is simple enough that it can be implemented and analysed without advanced mathematics like stochastic integration or Itô calculus, yet it is complicated enough to reflect a financial market. In particular, it allows us to easily understand concepts like risk-neutral measures and hedging strategies.

In this chapter we will review the basic knowledge of continuous probability theory and stochastic processes. We will take a look at general probability spaces and random variables as well as convergence of random variables in Section 6.1. In Section 6.2, we will take a look at stochastic processes and in Section 6.3, we will look at filtrations and conditional expected values in the general situation. A reader having a good understanding of those concepts can skip this chapter.

In this chapter we introduce some basic notions from finance. We explain the assumptions on financial markets which will be used in the rest of the book, and define key concepts such as arbitrage.

This chapter examines the way in which compensation is assessed for the purposes of breaches of an investment treaty. It considers the Hull Formula of gauging compensation, which focuses on market value, and the competing Calvo Doctrine. The chapter also explores the difficulties associated with valuing assets and emerging issues in relation to claims of moral damages.

In this section we study a more general discrete model, of which the binomial model is a special case. This model is called the finite market model. As for the binomial model, we are interested in the arbitrage-free price of a contingent claim. To study this question, we introduced two important tools in Chapter 3.