Effective risk management requires adequate risk measurement. A basic problem herein is the quantification of market risks: what is the overall effect on a portfolio if market rates change? First, a mathematical problem statement is given and the concept of `Maximum Loss' (ML) is introduced as a...

A new kind of proper efficiency, namely strong efficiency, is introduced in a locally convex space. Strong efficiency generalizes Borwein's super efficiency and refines other proper efficiency. We provide a scalar characterization for strongly efficient points and study the section property and...

This paper studies the consumption and portfolio selection problem of an agent who is liquidity constrained and has uninsurable income risk in a discrete time setting. It gives properties of optimal policies and presents numerical solutions. The paper, in particular, shows that liquidity...

For a single server loss system with finite waiting room with Poisson arrivals and deterministic service times we compute the optimal admission control rule when additionally to the queue length the residual service time is considered as a decision variable. The reward function is of a rather...

It is shown that the two machine preemptive job-shop problem with mean flow-time or makespan objective function and three jobs is NP-hard. This contrasts the fact that the nonpreemptive versions of these problems are polynomially solvable if the number of jobs is arbitrary but fixed. It is also...

In this paper, we study the problem of finding the minimal initial capital (i.e. super-replication value) needed in order to hedge (without risk) European contingent claims in a Markov setting under proportional transaction costs. The main result is that the cheapest (trivial) buy-and-hold...

For a vector-valued Markov decision process with discounted reward criterion, we study the structure of its value spaces defined for all initial states. At first we discuss the relationship between the value spaces, i.e. we verify a linking property for optimality. We next show that if the...

We consider three applications of impulse control in financial mathematics, a cash management problem, optimal control of an exchange rate, and portfolio optimisation under transaction costs. We sketch the different ways of solving these problems with the help of quasi-variational inequalities....

This paper analyses a game-theoretic model of Hi-Lo Poker. Bilateral-move N-round games are formulated and explicit solutions are derived. In the asymptotic case the form of optimal decision rule is derived and examples are provided. Copyright Springer-Verlag Berlin Heidelberg 1999

This work concerns controlled Markov chains with denumerable state space and discrete time parameter. The reward function is assumed to be≤0 and the performance of a control policy is measured by the expected total-reward criterion. Within this context, sufficient conditions are given so that...