Can the usage of a risky numeraire with a greater than risk free expected return reduce the capital requirements in a solvency test? I will show that this is not the case. In fact, under a reasonable technical condition, there exists no optimal numeraire which yields smaller capital requirements than any other numeraire. 1 Statement and Proof of the Result Can the usage of a risky numeraire wit...

We study a variant of the standard stochastic multi-armed bandit problem when one is not interested in the arm with the best mean, but instead in the arm maximising some coherent risk measure criterion. Further, we are studying the deviations of the regret instead of the less informative expected regret. We provide an algorithm, called RA-UCB to solve this problem, together with a high probabil...

We formulate a risk-averse two-stage stochastic linear programming problem in which unresolved uncertainty remains after the second stage. The objective function is formulated as a composition of conditional risk measures. We analyze properties of the problem and derive necessary and sufficient optimality conditions. Next, we construct two decomposition methods for solving the problem. The firs...

We consider the incorporation of a time-consistent coherent risk measure into a multi-stage stochastic programming model, so that the model can be solved using a SDDP-type algorithm. We describe the implementation of this algorithm, and study the solutions it gives for an application of hydro-thermal scheduling in the New Zealand electricity system. The performance of policies using this risk m...

Fair pricing of embedded options in life insurance contracts is usually conducted by using risk-neutral valuation. This pricing framework assumes a perfect hedging strategy, which insurance companies can hardly pursue in practice. In this paper, we extend the risk-neutral valuation concept with a risk measurement approach. We accomplish this by first calibrating contract parameters that lead to...

We present a general measure of risk that is rooted in behavioral considerations about the way individuals value uncertain outcomes, and that fulfills fundamental requirements for prescriptive use. The psychological postulate is that, in contemplating a risky situation, individuals care about how they will come out relative to all prospective outcomes of the situation, not just a specific bench...

Coherent and convex risk measures, Choquet expectation and Peng’s g-expectation are all generalizations of mathematical expectation. All have been widely used to assess financial riskiness under uncertainty. In this paper, we investigate differences amongst these risk measures and expectations. For this purpose, we constrain our attention of coherent and convex risk measures, and Choquet expect...

We study the general problem of an agent wishing to minimize the risk of a position at a fixed date. The agent trades in a market with a risky asset, with incomplete information, proportional transaction costs, and possibly constraints on strategies. In particular, this framework includes the problems of hedging contingent claims and maximizing utility from wealth. We obtain a minimization prob...

Expected Shortfall (ES) in several variants has been proposed as remedy for the deficiencies of Value-at-Risk (VaR) which in general is not a coherent risk measure. In fact, most definitions of ES lead to the same results when applied to continuous loss distributions. Differences may appear when the underlying loss distributions have discontinuities. In this case even the coherence property of ...

We consider the problem of optimally determining an investment portfolio for an energy company owning a network of gas pipelines, and in charge of purchasing, selling and distributing gas. We propose a two stage stochastic investment model which hedges risk by means of Conditional Value at Risk constraints. The model, solved by a decomposition method, is assessed on a real-life case, of a Brazi...