Application of a general risk management model to portfolio optimization problems with elliptical distributed returns for risk neutral and risk averse decision makers.

We discuss a class of risk measures for portfolio optimization with linear loss functions, where the random returns of financial instruments have a multivariate elliptical distribution. Under this setting we pay special attention to two risk measures, Value-at-Risk and Conditional-Value-at-Risk and differentiate between risk neutral and risk averse decision makers. When the so-called disutility function is taken as the identity function, the optimization problem is solved for a risk neutral investor. In this case, the optimal solutions of the two portfolio problems using the Value-at-Risk and Conditional-Value-at-Risk measures are the same as the solution of the classical Markowitz model. We adapt an existing less known finite algorithm to solve the Markowitz model. Its application within finance seems to be new and outperforms the standard quadratic programming procedure quadprog within MATLAB. When the disutility function is taken as a convex increasing function, the problem at hand is associated with a risk averse investor. If the Value-at-Risk is the choice of measure we show that the optimal solution does not differ from the risk neutral case. However, when Conditional-Value-at-Risk is preferred for the risk averse decision maker, the corresponding portfolio problem has a different optimal solution. In this case the used objective function can be easily approximated by Monte Carlo simulation. For the actual solution of the Markowitz model, we modify and implement the less known finite step algorithm and explain its core idea. After that we present numerical results to illustrate the effects of two disutility functions as well as to examine the convergence behavior of the Monte Carlo estimation approach.conditional value-at-risk;elliptical distributions;portfolio optimization;value-at-risk;disutility;linear loss functions

Application of a General Risk Management Model to Portfolio Optimization Problems with Elliptical Distributed Returns for Risk Neutral and Risk Averse Decision Makers

In this paper portfolio problems with linear loss functions and multivariate elliptical distributed returns are studied. We consider two risk measures, Value-at-Risk and Conditional-Value-at-Risk, and two types of decision makers, risk neutral and risk averse. For Value-at-Risk, we show that the optimal solution does not change with the type of decision maker. However, this observation is not true for Conditional-Value-at-Risk. We then show for Conditional-Value-at-Risk that the objective function can be approximated by Monte Carlo simulation using only a univariate distribution. To solve the equivalent Markowitz model, we modify and implement a finite step algorithm. Finally, a numerical study is conducted.Conditional value-at-risk;Disutility;Elliptical distributions;Linear loss functions;Portfolio optimization;Value-at-risk

Risk measures and their applications in asset management

Several approaches exist to model decision making under risk, where risk can be broadly defined as the effect of variability of random outcomes. One of the main approaches in the practice of decision making under risk uses mean-risk models; one such well-known is the classical Markowitz model, where variance is used as risk measure. Along this line, we consider a portfolio selection problem, where the asset returns have an elliptical distribution. We mainly focus on portfolio optimization models constructing portfolios with minimal risk, provided that a prescribed expected return level is attained. In particular, we model the risk by using Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). After reviewing the main properties of VaR and CVaR, we present short proofs to some of the well-known results. Finally, we describe a computationally efficient solution algorithm and present numerical results.conditional value-at-risk;elliptical distributions;mean-risk;portfolio optimization;value-at-risk

Rare Event Simulation Techniques for Stochastic Design Problems in Markovian Setting

Tijms, H.C. [Promotor]Ridder, A.A.N. [Copromotor

Application of a General Risk Management Model to Portfolio Optimization Problems with Elliptical Distributed Returns for Risk Neutral and Risk Averse Decision Makers

In this paper portfolio problems with linear loss functions and multivariate elliptical distributed returns are studied. We consider two risk measures, Value-at-Risk and Conditional-Value-at-Risk, and two types of decision makers, risk neutral and risk averse. For Value-at-Risk, we show that the optimal solution does not change with the type of decision maker. However, this observation is not true for C

Risk measures and their applications in asset management

Several approaches exist to model decision making under risk, where risk can be broadly defined as the effect of variability of random outcomes. One of the main approaches in the practice of decision making under risk uses mean-risk models; one such well-known is the classical Markowitz model, where variance is used as risk measure. Along this line, we consider a portfolio selection problem, where the asset returns have an elliptical distribution. We mainly focus on portfolio optimization models constructing portfolios with minimal risk, provided that a prescribed expected return level is attained. In particular, we model the risk by using Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). After reviewing the main properties of VaR and CVaR, we present short proofs to some of the well-known results. Finally, we describe a computationally efficient solution algorithm and present numerical results

From product recommendation to cyber-attack prediction: generating attack graphs and predicting future attacks

Modern information society depends on reliable functionality of information systems infrastructure, while at the same time the number of cyber-attacks has been increasing over the years and damages have been caused. Furthermore, graphs can be used to show paths than can be exploited by attackers to intrude into systems and gain unauthorized access through vulnerability exploitation. This paper presents a method that builds attack graphs using data supplied from the maritime supply chain infrastructure. The method delivers all possible paths that can be exploited to gain access. Then, a recommendation system is utilized to make predictions about future attack steps within the network. We show that recommender systems can be used in cyber defense by predicting attacks. The goal of this paper is to identify attack paths and show how a recommendation method can be used to classify future cyber-attacks in terms of risk management. The proposed method has been experimentally evaluated and validated, with the results showing that it is both practical and effective

Effects of intra-abdominal sepsis on atherosclerosis in mice

Introduction: Sepsis and other infections are associated with late cardiovascular events. Although persistent inflammation is implicated, a causal relationship has not been established. We tested whether sepsis causes vascular inflammation and accelerates atherosclerosis.Methods: We performed prospective, randomized animal studies at a university research laboratory involving adult male ApoE-deficient (ApoE-/-) and young C57B/L6 wild-type (WT) mice. In the primary study conducted to determine whether sepsis accelerates atherosclerosis, we fed ApoE-/- mice (N = 46) an atherogenic diet for 4 months and then performed cecal ligation and puncture (CLP), followed by antibiotic therapy and fluid resuscitation or a sham operation. We followed mice for up to an additional 5 months and assessed atheroma in the descending aorta and root of the aorta. We also exposed 32 young WT mice to CLP or sham operation and followed them for 5 days to determine the effects of sepsis on vascular inflammation.Results: ApoE-/- mice that underwent CLP had reduced activity during the first 14 days (38% reduction compared to sham; P < 0.001) and sustained weight loss compared to the sham-operated mice (-6% versus +9% change in weight after CLP or sham surgery to 5 months; P < 0.001). Despite their weight loss, CLP mice had increased atheroma (46% by 3 months and 41% increase in aortic surface area by 5 months; P = 0.03 and P = 0.004, respectively) with increased macrophage infiltration into atheroma as assessed by immunofluorescence microscopy (0.52 relative fluorescence units (rfu) versus 0.97 rfu; P = 0.04). At 5 months, peritoneal cultures were negative; however, CLP mice had elevated serum levels of interleukin 6 (IL-6) and IL-10 (each at P < 0.05). WT mice that underwent CLP had increased expression of intercellular adhesion molecule 1 in the aortic lumen versus sham at 24 hours (P = 0.01) that persisted at 120 hours (P = 0.006). Inflammatory and adhesion genes (tumor necrosis factor α, chemokine (C-C motif) ligand 2 and vascular cell adhesion molecule 1) and the adhesion assay, a functional measure of endothelial activation, were elevated at 72 hours and 120 hours in mice that underwent CLP versus sham-operations (all at P <0.05).Conclusions: Using a combination of existing murine models for atherosclerosis and sepsis, we found that CLP, a model of intra-abdominal sepsis, accelerates atheroma development. Accelerated atheroma burden was associated with prolonged systemic, endothelial and intimal inflammation and was not explained by ongoing infection. These findings support observations in humans and demonstrate the feasibility of a long-term follow-up murine model of sepsis