We propose a uni ed analysis of a whole spectrum of no-arbitrage conditions for nancial market models based on continuous semimartingales. In particular, we focus on no-arbitrage conditions weaker than the classical notions of No Arbitrage and No Free Lunch with Vanishing Risk. We provide a complete characterisation of all no-arbitrage conditions, linking their validity to the existence and to ...

This paper is a sequel to Kurano et al [9], [10], in which the fuzzy perceptive models for optimal stopping or discounted Markov decision process are proposed and the methods of computing the corresponding fuzzy perceptive values are given. Here, we deal with the average case for Markov decisin processes with fuzzy perceptive transition matrices and characterize the optimal average expected rew...

We introduce an algebraic operator framework to study discounted penalty functions in renewal risk models. For inter-arrival and claim size distributions with rational Laplace transform, the usual integral equation is transformed into a boundary value problem, which is solved by symbolic techniques. The factorization of the differential operator can be lifted to the level of boundary value prob...

In this paper, we consider a fairly large class of dependent Sparre Andersen risk models where the claim sizes belong to the class of Coxian distributions. We analyze the Gerber-Shiu discounted penalty function when the penalty function depends on the deficit at ruin. We show that the system of equations needed to solve for this quantity is surprisingly simple. Various applications of this resu...

Much of the research on human delay and probability discounting involves the use of hypothetical outcomes, in which participants indicate preferences for outcomes but do not receive them. Research generally shows that hypothetical and potentially real outcomes are discounted at similar rates. One study, however, shows that potentially real cigarettes are discounted more steeply than hypothetica...

We consider risk minimization problems for Markov decision processes. From a standpoint of making the risk of random reward variable at each time as small as possible, a risk measure is introduced using conditional value-at-risk for random immediate reward variables in Markov decision processes, under whose risk measure criteria the risk-optimal policies are characterized by the optimality equa...

This supplement has three parts. The first part considers the family of power function distributions F(v)= vα with support [0 1].1 The second part considers a two-period model with general distributions. It is shown that cutoffs (and, hence, the sum of discounted payoffs) can be uniformly ranked. In the third part, we discuss the technical difficulties associated with ranking the equilibrium cu...

We consider a minimum-cost dynamic network-flow problem on a very special network. This network flow problem models an infinite-horizon, lot-sizing problem with deterministic demand and periodic data. We permit two different objectives: minimize long-run average-cost per period and minimize the discounted cost. In both cases we give polynomial algorithms when certain arc costs are fixed charge ...

We study a class of discounted, infinite horizon stochastic games with public and private signals and strategic complementarities. Using monotone operators defined on the function space of values and strategies (equipped with a product order), we prove existence of a stationary Markov–Nash equilibrium via constructive methods. In addition, we provide monotone comparative statics results for ord...