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In many sequential decision-making problems we may want to manage risk by minimizing some measure of variability in costs in addition to minimizing a standard criterion. Conditional value-at-risk (CVaR) is a relatively new risk measure that…
Considering non-stationary environments in online optimization enables decision-maker to effectively adapt to changes and improve its performance over time. In such cases, it is favorable to adopt a strategy that minimizes the negative…
Optimizing risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) of a general loss distribution is usually difficult, because 1) the loss function might lack structural properties such as convexity or…
Optimal portfolio allocation is often formulated as a constrained risk problem, where one aims to minimize a risk measure subject to some performance constraints. This paper presents new Bayesian Optimization algorithms for such constrained…
We study the optimal portfolio allocation problem from a Bayesian perspective using value at risk (VaR) and conditional value at risk (CVaR) as risk measures. By applying the posterior predictive distribution for the future portfolio…
The popularity of Conditional Value-at-Risk (CVaR), a risk functional from finance, has been growing in the control systems community due to its intuitive interpretation and axiomatic foundation. We consider a nonstandard optimal control…
This paper proposes a safety analysis method that facilitates a tunable balance between the worst-case and risk-neutral perspectives. First, we define a risk-sensitive safe set to specify the degree of safety attained by a stochastic…
The problem of finding the optimal portfolio for investors is called the portfolio optimization problem. Such problem mainly concerns the expectation and variability of return (i.e., mean and variance). Although the variance would be the…
We show how to reduce the problem of computing VaR and CVaR with Student T return distributions to evaluation of analytical functions of the moments. This allows an analysis of the risk properties of systems to be carefully attributed…
We consider the portfolio optimization with risk measured by conditional value-at-risk, based on the stress event of chosen asset being equal to the opposite of its value-at-risk level, under the normality assumption. Solvability conditions…
The entropic value-at-risk (EVaR) is a new coherent risk measure, which is an upper bound for both the value-at-risk (VaR) and conditional value-at-risk (CVaR). As important properties, the EVaR is strongly monotone over its domain and…
We propose a risk-averse statistical learning framework wherein the performance of a learning algorithm is evaluated by the conditional value-at-risk (CVaR) of losses rather than the expected loss. We devise algorithms based on stochastic…
The ability to make optimal decisions under uncertainty remains important across a variety of disciplines from portfolio management to power engineering. This generally implies applying some safety margins on uncertain parameters that may…
Conditional Value at Risk (CVaR) is a prominent risk measure that is being used extensively in various domains. We develop a new formula for the gradient of the CVaR in the form of a conditional expectation. Based on this formula, we…
We consider a liquidation problem in which a risk-averse trader tries to liquidate a fixed quantity of an asset in the presence of market impact and random price fluctuations. The trader encounters a trade-off between the transaction costs…
We use a replica approach to deal with portfolio optimization problems. A given risk measure is minimized using empirical estimates of asset values correlations. We study the phase transition which happens when the time series is too short…
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…
Managing insurance and financial risk when data is limited is a key task in the insurance industry. In this paper, we focus on cases where the risk distribution is modeled as a mixture with some components estimable to high precision or…
This paper proposes analytic forms of portfolio CoVaR and CoCVaR on the normal tempered stable market model. Since CoCVaR captures the relative risk of the portfolio with respect to a benchmark return, we apply it to the relative portfolio…
In this paper we address the problem of decision making within a Markov decision process (MDP) framework where risk and modeling errors are taken into account. Our approach is to minimize a risk-sensitive conditional-value-at-risk (CVaR)…