Timothy Johnson

Buy‐Low and Sell‐High Investment Strategies

Buy-low and sell-high investment strategies are a recurrent theme in the considerations of many investors. In this paper, we consider an investor who aims at maximizing the expected discounted cash-flow that can be generated by sequentially buying and selling one share of a given asset at fixed transaction costs. We model the underlying asset price by means of a general one-dimensional Ito diffusion X, we solve the resulting stochastic control problem in a closed analytic form, and we completely characterize the optimal strategy. In particular, we show that, if 0 is a natural boundary point of X, e.g., if X is a geometric Brownian motion, then it is never optimal to sequentially buy and sell. On the other hand, we prove that, if 0 is an entrance point of X, e.g., if X is a mean-reverting constant elasticity of variance (CEV) process, then it may be optimal to sequentially buy and sell, depending on the problem data.

The explicit solution to a sequential switching problem with non-smooth data

We consider the problem faced by a decision maker who can switch between two random payoff flows. Each of these payoff flows is an additive functional of a general 1D Itô diffusion. There are no bounds on the number or on the frequency of the times at which the decision maker can switch, but each switching incurs a cost, which may depend on the underlying diffusion. The objective of the decision maker is to select a sequence of switching times that maximizes the associated expected discounted payoff flow. In this context, we develop and study a model in the presence of assumptions that involve minimal smoothness requirements from the running payoff and switching cost functions, but which guarantee that the optimal strategies have relatively simple forms. In particular, we derive a complete and explicit characterization of the decision makers optimal tactics, which can take qualitatively different forms, depending on the problem data.

The solution to a second order linear ordinary differential equation with a non-homogeneous term that is a measure

We consider the solvability of the ordinary differential equation (ODE) inside an interval , where σ, b, r are given functions and h is a locally finite measure. This ODE is associated with the Hamilton–Jacobi–Bellman (HJB) equations arising in the study of a wide range of stochastic optimisation problems. These problems are motivated by numerous applications and include optimal stopping, singular stochastic control and impulse stochastic control models in which the state process is given by a one-dimensional Itô diffusion. Under general conditions, we derive both analytic and probabilistic expressions for the solution to equation (1) that is required by the analysis of the relevant stochastic control models. We also establish a number of properties that are important for applications.

Reciprocity as a Foundation of Financial Economics

This paper argues that the subsistence of the fundamental theorem of contemporary financial mathematics is the ethical concept ‘reciprocity’. The argument is based on identifying an equivalence between the contemporary, and ostensibly ‘value neutral’, Fundamental Theory of Asset Pricing with theories of mathematical probability that emerged in the seventeenth century in the context of the ethical assessment of commercial contracts in a framework of Aristotelian ethics. This observation, the main claim of the paper, is justified on the basis of results from the Ultimatum Game and is analysed within a framework of Pragmatic philosophy. The analysis leads to the explanatory hypothesis that markets are centres of communicative action with reciprocity as a rule of discourse. The purpose of the paper is to reorientate financial economics to emphasise the objectives of cooperation and social cohesion and to this end, we offer specific policy advice.

Validation of a dynamic control model to simulate investment cycles in electricity generating capacity

The ability of the liberalised energy markets to trigger investment in the generation capacity required to maintain an acceptable level of security of supply risk has been - and will continue to be - a topic of much debate.

A Methodology to Assess the Economic Impact of Power Storage Technologies

We present a methodology for assessing the economic impact of power storage technologies. The methodology is founded on classical approaches to the optimal stopping of stochastic processes but involves an innovation that circumvents the need to, \emph{ex ante}, identify the form of the driving process; the approach works directly on observed data and so avoids model risks. Power storage is regarded as a complement to the variable output of of renewable energy generators, and is therefore important in contributing to the reduction of carbon intensive power generation. Our aim is to present a methodology suitable for use by policy makers that is simple to maintain, adaptable to different technologies and easy to interpret the results. The approach is shown to have benefits over standard techniques and is able to identify a viable optimal strategy for a fictitious storage facility operating in the UK power market.

Discourse Ethics for Debt Markets

This article develops a pragmatic theory of finance in which markets are considered to be centres of communicative action in the face of uncertainty. This contrasts with the conventional approach that portrays markets as centres of strategic action in the face of scarcity. The argument follows Habermas and entails that a financial market must address the truthfulness, truth, and rightness of the statements made by its participants (i.e., the prices quoted). I claim that these discursive norms have been implicit in historical financial markets as expressed in the norms of sincerity, reciprocity, and charity. I conclude by proposing that ‘trust’ in commerce is a synthesis of the three discursive norms. The motivation of the article is to address the crisis of legitimacy that the financial system is experiencing, particularly in the United Kingdom (UK) and the United States (US).

Teaching Reciprocity as the Foundation of Financial Economics

The financial crises that have occurred since 2006 have been associated with a degradation in financial ethics. Since the teaching of derivative pricing is often undertaken in the context of abstract mathematics, the question arises of the role of mathematics in supporting financial ethics. At the heart of the Fundamental Theorem of Asset Pricing, the foundational theory of mathematical approaches to derivative pricing, is the concept of reciprocity. This chapter shows how reciprocity was reliant upon the emergence of probability theory before 1700, where a risk-less profit was seen as illicit. The chapter finishes with a discussion of how this ethical approach to financial economics is presented to undergraduate and, more advanced, post-graduate students.

Finance and Ethics in Medieval Europe

This chapter introduces the role of reciprocity in supporting social cohesion, which was introduced by Aristotle in his discussion of justice in Nicomachean Ethics. Aristotle’s discussion inspired the Scholastic Albert the Great to reconsider the mathematical concept of measurement that led to the mathematisation of science. It also prompted Thomas Aquinas and Pierre Jean Olivi to address issues of justice in commerce that prompted a refinement of the doctrine on usury and the quantification of probability.

The Philosophical Basis of Modernity

The roots of empiricism in Baconian science are described. Cartesian rationalism made a break with Scholasticism in seeking to establish certainty in the context of the uncertainty generated by the continental wars of the period. Hobbes employed the deductive method to develop a unique, and pessimistic, philosophy. Hobbes rejection of the possibility of free will, breaking with Scholastic attitudes, is taken up by Spinoza, who concluded that the aim of humans was to achieve a divine perspective from which free will was redundant because knowledge is certain. Locke’s empiricism addressed the problem of doubt by requiring an individual to ascertain the origins of an idea in experience. The immediate consequence is that Lockean knowledge never claims to be certain and so trust must be established.