Volume 2, Issue 3-4

In the deterministic context a series of well established results allow to reformulate delay differential equations (DDEs) as evolution equations in infinite dimensional spaces. Several models in the theoretical economic literature have been studied using this reformulation. On the other hand, in the stochastic case only few results of this kind are available and only for specific problems. The contribution of the present letter is to present a way to reformulate in infinite dimension a prototype controlled stochastic DDE, where the control variable appears delayed in the diffusion term. As application, we present a model for quadratic risk minimization hedging of European options with execution delay and a time-to-build model with shock. Some comments concerning the possible employment of the dynamic programming after the reformulation in infinite dimension conclude the letter.

We investigate a solution for the option pricing partial differential equation (PDE) in a market suffering from a financial crisis. The post-crash model assumes that the volatility is stochastic. It is an extension of the famous Black and Scholes model. Therefore, the option pricing PDE for the crisis model is a generalization of the Black and Scholes PDE. However, to the best knowledge, it does not have a closed form solution for the general case. In this paper, we provide a solution for the pricing PDE of a European option during financial crisis using the homotopy analysis method.

This paper investigates a market with vertical product differentiation, where both qualities and consumers are represented by uni-dimensional intervals. Our framework deals with a continuum of consumers. We investigate the consumers' self selection in a product quality model under an offer-spectrum of quality-price pairs. We show the conditions under which there will be no market failure.

We suggest in this paper that voting in political systems can be profitably analysed using complex system analysis. We discuss how we can capture the complexity of voting behaviour by applying graph theory in networks and we develop a simplified theoretical model of voting choice adopting the basic heuristics of the behavioural decision theory. We feel that such a complex systems approach provides a superior basis for understanding voting behaviour compared to standard political economy analysis.

The choice of time as a discrete or continuous variable may radically affect the stability of equilibrium in an endogenous growth model with durable consumption. In the continuous-time model the steady state is locally saddle-path stable with monotonic convergence. However, in the discrete-time model the steady state may be unstable or saddle-path stable with monotonic or oscillatory convergence.

It is well known that the core of an exchange market with indivisible goods is always non empty, although it may contain Pareto inefficient allocations. The strict core solves this shortcoming when indifferences are not allowed, but when agents' preferences are weak orders the strict core may be empty. On the other hand, when indifferences are allowed, the core or the strict core may fail to be stable sets, in the von Neumann and Morgenstern sense. We introduce a new solution concept that improves the behaviour of the strict core, in the sense that it solves the emptiness problem of the strict core when indifferences are allowed in the individuals' preferences and whenever the strict core is non-empty, our solution is included in it. We define our proposal, the MS-set , by using a stability property ( m-stability ) that the strict core fulfills. Finally, we provide a min-max interpretation for this new solution.

We consider a perishable inventory system with bonus service for certain customers. The maximum inventory level is S . The ordering policy is (0,  S ) policy and the lead time is zero. The life time of each items is assumed to be exponential. Arrivals of customers follow a Poisson process with parameter λ . Arriving customers form a single waiting line based on the order of their arrivals. The capacity of the waiting line is restricted to M including the one being served. The first N  ≥ 1 customers who arrive after the system becomes empty must wait for service to begin. We have assumed that these N customers received an additional service, called bonus service, in addition to the essential service rendered to all customers. The service times are exponentially distributed. An arriving customer who finds the server busy or waiting area size ≥  N , proceeds to the waiting area with probability p and is lost forever with probability (1 −  p ). The Laplace–Stieltjes transform of the waiting time of the tagged customer is derived. The joint probability distribution of the number of customers in the waiting area and the inventory level is obtained for the steady state case. Some important system performance measures and the long-run total expected cost rate are derived in the steady state.