Markov risk mappings and risk-sensitive optimal stopping

In contrast to the analytic approach to risk for Markov chains based on transition risk mappings, we introduce a probabilistic setting based on a novel concept of regular conditional risk mapping with Markov update rule. We confirm that the Markov property holds for the standard measures of risk used in practice such as Value at Risk and Average Value at Risk. We analyse the dual representation for convex Markovian risk mappings and a representation in terms of their acceptance sets. The Markov property is formulated in several equivalent versions including a strong version, opening up additional risk-sensitive optimisation problems such as optimal stopping with exercise lag and optimal prediction. We demonstrate how such problems can be reduced to a risk-sensitive optimal stopping problem with intermediate costs, and derive the dynamic programming equations for the latter. Finally, we show how our results can be extended to partially observable Markov processes.Comment: 29 pages. New: extension of one-step ahead Markov property to entire "future", Markov property in terms of acceptance sets, VaR and AVaR examples, convex Markov risk mappings, application to optimal stopping with exercise lag. Notable changes: Stopping cost in the partially observable optimal stopping problem can depend on the unobservable stat

Measurement of uncertainty costs with dynamic traffic simulations

Non-recurrent congestion in transportation networks occurs as a consequence of stochastic factors affecting demand and supply. Intelligent Transportation Systems such as Advanced Traveler Information Systems (ATIS) and Advanced Traffic Management Systems (ATMS) are designed in order to reduce the impacts of non-recurrent congestion by providing information to a fraction of users or by controlling the variability of traffic flows. For these reasons, the design of ATIS and ATMS requires reliable forecast of non-recurrent congestion. This paper proposes a new method to measure the impacts of non-recurrent congestion on travel costs by taking risk aversion into account. The traffic model is based on the dynamic traffic simulations model METROPOLIS. Incidents are generated randomly by reducing the capacity of the network. Users can instantaneously adapt to the unexpected travel conditions or can also change their behavior via a day-to-day adjustment process. Comparisons with incident-free simulations provide a benchmark for potential travel time savings that can be brought in by a state-of-the-art information system. We measure the impact of variable travel conditions by describing the willingness to pay to avoid risky or unreliable journeys. Indeed, for risk averse drivers, any uncertainty corresponds to a utility loss. This utility loss is computed for several levels of network disruption. The main results of the paper is that the utility loss due to uncertainty is of the same order of magnitude as the total travel costs.

Dynamic Asset Allocation with Regime Shifts and Long Horizon CVaR-Constraints

We analyse portfolio policies for investors who invest optimally for given investment horizons with respect to Conditional Value-at-Risk constraints. We account for nonnormally distributed, skewed, and leptokurtic asset return distributions due to regime shifts. The focus is on standard CRRA utility with a money back guarantee at maturity, which is often augmented to individual retirement plans. Optimal solutions for the unconstrained as well as the constrained policy are provided and examined for risk management costs calculated as welfare losses. Our results confirm previous findings that money back guarantees yield mild downside protection at low economic costs for most long term investors