Risk and Decision Analysis

This paper examines the relationship between option pricing models that use stochastic dominance concepts in discrete time, and the traditional arbitrage-based continuous time models. It derives multiperiod discrete time index option bounds based on stochastic dominance considerations for a risk-averse investor holding only the underlying asset, the riskless asset and (possibly) the option for any type of underlying asset distribution in which the market index is the single state variable. It then considers the limit behavior of these bounds as trading becomes progressively more frequent and the underlying asset tends to continuous time diffusion. It is shown that these bounds tend to the unique Black–Scholes–Merton option price. This result is extended to equity options by assuming a linear CAPM-type relationship between index and equity returns.

Financial Regulation is a socio-political and economic need that has risks and a price. Globalization, the growth financial institutions, both national and a-national, complex financial futures and other products, financial chains, intermediaries and networks, etc. have increased the complexity of finance. Not least, a growth of financial technologies (both in hardware and software) has amplified opportunities to profit as well as challenged regulators and regulation. A regulatory response, following the 2007–2009 financial crisis, based on the Dodd–Frank act has at the same time generated hundreds of regulations, some misunderstood and misinterpreted by an endless series of court cases. These developments have rendered compliance, both complex and at best costly and elusive. While an extensive research on regulation has focused on the implications of one or another regulatory edict, little research has focused on defining non-compliance and defining controls to an increasingly strategic regulatory environment. The purpose of this paper is to raise a number of regulation risks and provide a strategic and statistical (gaming) approach to regulation and its control based on a “regulation game” of a regulated financial institution and its regulators. Unlike previous studies focused on the scope and the intent of regulation, this paper calls attention to the implications of controls.

Ensuring appropriate user access to information is a key objective of information security on a computer network. We propose a solution in which an individual user is assigned a universal trust score determined by applying the same model financial institutions use to determine an individual's credit risk score. This universal trust score is combined with the Bell–La Padula model to control the individual's access to information across multiple assured information sharing systems.

In this paper uncertainty is defined as non-uniqueness of projection of a preference on consequences onto the set of preferences on acts in a choice problem. Such definition of uncertainty seems natural, but it is not very well known despite being compatible with M. Allais principle of internal coherence [Econometrica 21(4) (1953), 503–546]. It is shown that absence of arbitrage opportunity, in the sense of the Arrow–Debreu model of securities market with a risk-less asset, represents an example and a particular case of existence of uncertainty, defined in the above sense.

This paper analyzes the problem of starting and stopping a Cox–Ingersoll–Ross (CIR) process with fixed costs. In addition, we also study a related optimal switching problem that involves an infinite sequence of starts and stops. We establish the conditions under which the starting–stopping and switching problems admit the same optimal starting and/or stopping strategies. We rigorously prove that the optimal starting and stopping strategies are of threshold type, and give the analytical expressions for the value functions in terms of confluent hypergeometric functions. Numerical examples are provided to illustrate the dependence of timing strategies on model parameters and transaction costs.