The recent experience from the global financial crisis has raised serious doubts about the accuracy of standard risk measures as a tool to quantify extreme downward risks. Standard risk measures are subject to a “model risk” due to the specification and estimation uncertainty. We propose a...

We introduce a family of Capital allocation rules (C.A.R) based on the dual representation for risk measures and inspired to the Aumann-Shapley allocation principle. These rules extend the one of Denault and Kalkbrener (for coherent risk measures) and the one of Tsanakas (convex case), to the...

We study the impact of market contagion on portfolio management. To model possible recurrence in the arrival of extreme events, we equip classic Poisson jumps with long memory via past-weighted randomization of the likelihood of their occurrences (Hawkes processes). Within this framework, we...

This paper proposes an intuitive and flexible framework to quantify liquidation risk for financial institutions. We develop a model where the "fundamental" dynamics of assets is modified by price impact from fund liquidations (if any). We characterize mathematically the liquidation schedule of...

Financial institutions have to satisfy capital adequacy tests required, e.g., by the Basel Accords for banks or by Solvency II for insurers. If the financial situation of an institution is tight, then it can happen that no reallocation of the initial endowment would pass the capital adequacy...

This paper considers the expected utility portfolio optimization problem with initial-time and intermediate-time Value-at-Risk (VaR) constraints on terminal wealth. We derive the closed-form solutions which are optimal among all feasible strategies at initial time, i.e., precommitted strategies....

Stock investment is one option of investment choice with risks. Investors can reduce their risk by combining several stocks and then forming a portfolio. One method to form an optimal portfolio is by using the Constant Correlation Model (CCM) method. The CCM method focuses on the correlation...

The optimization of a large random portfolio under the Expected Shortfall risk measure with an ℓ₂ regularizer is carried out by analytical calculation. The regularizer reins in the large sample fluctuations and the concomitant divergent estimation error, and eliminates the phase transition...

The risk of a future payoff is commonly quantified by calculating the costs of a hedging portfolio such that the resulting position is acceptable, i.e. that it passes a capital adequacy test. A multi-asset risk measure describes the minimal external capital which has to be raised into multiple...