W study optimization problems with value-at-risk (VaR) constraints. Because it lacks subadditivity, VaR is not a coherent risk measure and does not necessarily preserve the convexity. Thus, the problems we consider are typically not provably convex. As such, the conditional value-at-risk (CVaR) approximation is often used to handle such problems. Even though the CVaR approximation is known as t...

For many decision making problems under uncertainty, it is crucial to develop risk-averse models and specify the decision makers’ risk preferences based on multiple stochastic performance measures (or criteria). Incorporating such multivariate preference rules into optimization models is a fairly recent research area. Existing studies focus on extending univariate stochastic dominance rules to ...

Value-at-Risk (VaR) and Conditional-Value-at-Risk (CVaR) are two risk measures which are widely used in the practice of risk management. This paper deals with the problem of estimating both VaR and CVaR using stochastic approximation (with decreasing steps): we propose a first Robbins-Monro (RM) procedure based on Rockafellar-Uryasev’s identity for the CVaR. Convergence rate of this algorithm t...

Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) are two risk measures which are widely used in the practice of risk management. This paper deals with the problem of computing both VaR and CVaR using stochastic approximation (with decreasing steps): we propose a first Robbins-Monro procedure based on Rockaffelar-Uryasev’s identity for the CVaR. The convergence rate of this algorithm to ...

Investasi saham adalah kegiatan menanamkan sejumlah dana pada suatu perusahaan dengan tujuan mendapatkan keuntungan di masa depan. Seorang investor umumnya melihat return untuk berinvestasi, tetapi harga mengalami perubahan yang tidak terduga sehingga ada risiko mengikuti. Analisis perlu dilakukan menghindari kerugian akan datang. Penelitian ini mengetahui dan mengestimasi menggunakan Condition...

This paper investigates a risk-averse inventory model by balancing the expected profit and conditional value-at-risk (CVaR) in a newsvendor model setting. We find out that: i) The optimal order quantity is increasing in the shortage cost for both the CVaR only criterion and the tradeoff objective. ii) For the case of zero shortage cost, the optimal order quantity to the CVaR criterion or tradeo...

This note is focused on computational efficiency of the portfolio selection models based on the Conditional Value at Risk (CVaR) risk measure. The CVaR measure represents the mean shortfall at a specified confidence level and its optimization may be expressed with a Linear Programming (LP) model. The corresponding portfolio selection models can be solved with general purpose LP solvers. However...

<p style='text-indent:20px;'>This paper analyzes Conditional Value-at-Risk (CVaR) based partial hedging and its applications on equity-linked life insurance contracts in a Jump-Diffusion market model with transaction costs. A nonlinear differential equation (PDE) that an option value process inclusive of costs should satisfy is provided. In particular, the closed-form expression European ...

Worst-case risk measures refer to the calculation of the largest value for risk measures when only partial information of the underlying distribution is available. For the popular risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), it is now known that their worst-case counterparts can be evaluated in closed form when only the first two moments are known for the unde...

We study a risk-constrained version of the stochastic shortest path (SSP) problem, where the risk measure considered is Conditional Value-at-Risk (CVaR). We propose two algorithms that obtain a locally risk-optimal policy by employing four tools: stochastic approximation, mini batches, policy gradients and importance sampling. Both the algorithms incorporate a CVaR estimation procedure, along t...