In this paper, we extend a recently proposed scenario decomposition algorithm (Ahmed (2013)) for risk-neutral 0-1 stochastic programs to the risk-averse setting. Specifically, we consider risk-averse 0-1 stochastic programs with objective functions based on coherent risk measures. Using a dual representation of a coherent risk measure, we first derive an equivalent minimax reformulation of the ...

We evaluate conditional value-at-risk (CVaR) as a risk measure in data-driven portfolio optimization. We show that portfolios obtained by solving mean-CVaR and global minimum CVaR problems are unreliable due to estimation errors of CVaR and/or the mean, which are aggravated by optimization. This problem is exacerbated when the tail of the return distribution is made heavier. We conclude that CV...

In this paper, we consider the problem of optimal reinsurance design, when the risk is measured by a distortion risk measure and the premium is given by a distortion risk premium. First, we show how the optimal reinsurance design for the ceding company, the reinsurance company and the social planner can be formulated in the same way. Second, by introducing the “marginal indemnification function...

As a necessary requirement for multi-period risk measure, time consistency can be examined from two aspects: dynamic riskmeasure andoptimal investment policy. In this paper,we first study the relationship between the time consistency of dynamic risk measure and the time consistency of optimal investment policy and obtain the following conclusions: if the dynamic riskmapping is time consistent a...

In incomplete financial markets not every given contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by coherent risk measures, introduced by Artzner et al. [1]. The dynamic optimization problem of finding a self-financing strategy that minimizes the coherent risk of the shortfall can be split into a static optimization problem and...

This paper studies optimal risk redistribution between firms, such as banks or insurance companies. The introduction of the Basel II regulation and the Swiss Solvency Test (SST) has increased the use of risk measures to evaluate financial or insurance risk. We consider the case where firms use a distortion risk measure (also called dual utility) to evaluate risk. The paper first characterizes a...

We give a complete characterization of both comonotone and not comonotone coherent risk measures in the discrete finite probability space, where each outcome is equally likely. To the best of our knowledge, this is the first work that characterizes and distinguishes comonotone and not comonotone coherent risk measures via AVaR representation in the discrete finite probability space of equally l...

We consider a trader who wants to direct his portfolio towards a set of acceptable wealths given by a convex risk measure. We propose a black-box algorithm, whose inputs are the joint law of stock prices and the convex risk measure, and whose outputs are the numerical values of initial capital requirement and the functional form of a trading strategy to achieve acceptability. We also prove opti...

An application of the duality theory of linear optimization leads to the well known arbitrage pricing theorems of financial mathematics, namely, the equivalence between the absence of arbitrage and the existence of an equivalent martingale probability measure. The prices of contingent claims can then be calculated based on the set of martingale probability measures. Especially, in the incomplet...

We study the problem of optimally hedging exotic derivatives positions using a combination of dynamic trading strategies in underlying stocks, and static positions in vanilla options when the performance is quantified by a convex risk measure. We establish conditions for the existence of an optimal static position for general convex risk measures, and then analyze in detail the case of expected...