This paper deals with risk measurement and portfolio optimization under risk constraints. Firstly we give an overview of risk assessment from the viewpoint of risk theory, focusing on moment-based, distortion and spectral risk measures. We subsequently apply these ideas to an asset management...

We determine the optimal investment strategy in a Black-Scholes financial market to minimize the so-called probability of drawdown, namely, the probability that the value of an investment portfolio reaches some fixed proportion of its maximum value to date. We assume that the portfolio is...

Stochastic optimisation has found a fertile ground for applications in finance. One of the greatest challenges remains to incorporate a set of scenarios that accurately models the behaviour of financial markets, and in particular their behaviour during crashes and crises, without sacrificing the...

In this paper, a link between a time-consistent and a pre-commitment investment strategy is established. We define an implied investment target, which is implicitly contained in a time-consistent strategy at a given time step and wealth level. By imposing the implied investment target at the...

Investors often adopt mean-variance efficient portfolios for achieving superior risk-adjusted returns. However, such portfolios are sensitive to estimation errors, which affect portfolio performance. To understand the impact of estimation errors, I develop simple and intuitive formulas of the...

Scenario stress testing is a useful and increasingly popular approach to assess portfolio performance under different market conditions. In this paper we focus on how to incorporate stress scenario information directly in portfolio construction as additional constraints to control for potential...

We study a worst-case scenario approach to the stochastic dynamic programming problem, presenting a general probability-based framework and some properties of the arising Bellman-Isaacs equation which allow to obtain a closed-form analytic solution. We also adapt the results for a discrete...

We assess the effectiveness of various portfolio optimization strategies (only long allocations) applied to the components of the Euro Stoxx 50 index during the period 2002-2015. The sample under study contemplates episodes of high volatility and instability in financial markets, such as the...

We study the boundedness properties of the value function for a general worst-case scenario stochastic dynamic programming problem. For the portfolio selection problem,we present sufficient economically reasonable conditions for the finitness and uniform boundedness of the value function. The...

A portfolio of independent, but not identically distributed, returns is optimized under the variance risk measure, in the high-dimensional limit where the number N of the different assets in the portfolio and the sample size T are assumed large with their ratio r=N/T kept finite, with a ban on...