Related papers: On the equivalence between Value-at-Risk- and Expe…
We solve an expected utility-maximization problem with a Value-at-risk constraint on the terminal portfolio value in an incomplete financial market due to stochastic volatility. To derive the optimal investment strategy, we use the dynamic…
We study issues of robustness in the context of Quantitative Risk Management and Optimization. We develop a general methodology for determining whether a given risk measurement related optimization problem is robust, which we call…
Financial institutions have to allocate so-called "economic capital" in order to guarantee solvency to their clients and counter parties. Mathematically speaking, any methodology of allocating capital is a "risk measure", i.e. a function…
We consider the problems of estimation and optimization of two popular convex risk measures: utility-based shortfall risk (UBSR) and Optimized Certainty Equivalent (OCE) risk. We extend these risk measures to cover possibly unbounded random…
We consider market players with tail-risk-seeking behaviour as exemplified by the S-shaped utility introduced by Kahneman and Tversky. We argue that risk measures such as value at risk (VaR) and expected shortfall (ES) are ineffective in…
We consider an expected utility maximization problem where the utility function is not necessarily concave and the time horizon is uncertain. We establish a necessary and sufficient condition for the optimality for general non-concave…
It is well known that Expected Shortfall (also called Average Value-at-Risk) is a convex risk measure, i. e. Expected Shortfall of a convex linear combination of arbitrary risk positions is not greater than a convex linear combination with…
We study a continuous-time portfolio optimization problem under an explicit constraint on the Deviation Conditional Value-at-Risk (DCVaR), defined as the difference between the CVaR and the expected terminal wealth. While the mean-CVaR…
This paper solves a utility maximization problem under utility-based shortfall risk constraint, by proposing an approach using Lagrange multiplier and convex duality. Under mild conditions on the asymptotic elasticity of the utility…
We study the properties of Expected Shortfall from the point of view of financial risk management. This measure --- which emerges as a natural remedy in some cases where Value at Risk (VaR) is not able to distinguish portfolios which bear…
Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set…
This paper studies a finite-horizon portfolio selection problem with non-concave terminal utility and proportional transaction costs, in which the commonly used concavification principle for terminal value is no longer applicable. We…
This paper extends the utility maximization literature by combining partial information and (robust) regulatory constraints. Partial information is characterized by the fact that the stock price itself is observable by the optimizing…
We address the problem that classical risk measures may not detect the tail risk adequately. This can occur for instance due to averaging when calculating the Expected Shortfall. The current literature proposes the so-called adjusted…
We consider a collection of derivatives that depend on the price of an underlying asset at expiration or maturity. The absence of arbitrage is equivalent to the existence of a risk-neutral probability distribution on the price; in…
This paper studies a mean-risk portfolio choice problem for log-returns in a continuous-time, complete market. This is a growth-optimal problem with risk control. The risk of log-returns is measured by weighted Value-at-Risk (WVaR), which…
In this paper, we search for optimal portfolio strategies in the presence of various risk measure that are common in financial applications. Particularly, we deal with the static optimization problem with respect to Value at Risk, Expected…
We study a static portfolio optimization problem with two risk measures: a principle risk measure in the objective function and a secondary risk measure whose value is controlled in the constraints. This problem is of interest when it is…
The aims of this study are twofold. First, we consider an optimal risk allocation problem with non-convex preferences. By establishing an infimal representation for distortion risk measures, we give some necessary and sufficient conditions…
We introduce and study the main properties of a class of convex risk measures that refine Expected Shortfall by simultaneously controlling the expected losses associated with different portions of the tail distribution. The corresponding…