Abstract We present an optimization problem to determine the minimum capital requirement for a non-life insurance company. The imposes non-positive Conditional Value-at-Risk (CVaR) of insurer’s net loss and portfolio performance constraint. When expressing in semiparametric form, we demonstrate its convexity any integrable random variable representing liability. Furthermore, prove that function...

This article develops a new algorithm named TTRISK to solve high-dimensional risk-averse optimization problems governed by differential equations (ODEs and/or partial [PDEs]) under uncertainty. As an example, we focus on the so-called Conditional Value at Risk (CVaR), but approach is equally applicable other coherent risk measures. Both full and reduced space formulations are considered. The ba...

Minimizing VaR, as estimated from a set of scenarios, is a difficult integer programming problem. Solving the problem to optimality may demand using only a small number of scenarios, which leads to poor out-ofsample performance. A simple alternative is to minimize CVaR for several different quantile levels and then to select the optimized portfolio with the best out-of-sample VaR. We show that ...

This article considers a stochastic vehicle routing problem with probability constraints. The that customers are served before their (uncertain) deadlines must be higher than pre-specified target. It is unrealistic to expect the perfect knowledge on distributions of always available. To this end, we propose distributionally robust optimisation framework study worst bounds problem, which exploit...

Robust optimization is one of typical approaches to optimize a system with incomplete information and considerable uncertainty. The standard robust optimization problem minimizes maximum cost by focusing on the considerable worst case. In some application field, it is certainly important to consider the worst case among all considerable cases, but this min-max criterion tends to lead an overly ...

We study a first-order primal-dual subgradient method to optimize risk-constrained risk-penalized optimization problems, where risk is modeled via the popular conditional value at (CVaR) measure. The algorithm processes independent and identically distributed samples from underlying uncertainty in an online fashion, produces $\eta/\sqrt{K}$-approximately feasible optimal point within $K$ iterat...

In the circumstance that unexpected events lead to information asymmetry of sales costs, supplier risk aversion and stochastic price, this paper discusses internal law using an emergency quantity discount contract coordinate supply chain. First, Conditional Value at Risk (CVaR) model under condition symmetry is constructed. addition, extended game CVaR asymmetric costs solved. After that, simul...

We consider continuous-time stochastic optimal control problems featuring Conditional Valueat-Risk (CVaR) in the objective. The major difficulty in these problems arises from timeinconsistency, which prevents us from directly using dynamic programming. To resolve this challenge, we convert to an equivalent bilevel optimization problem in which the inner optimization problem is standard stochast...

One of the most important problems faced by every investor is asset allocation. An investor during making investment decisions has to search for equilibrium between risk and returns. Risk ‎and ‎return are uncertain parameters in ‎the ‎suggested portfolio optimization models and should be estimated to solve the‎problem. The estimation might‎ lead ‎to ‎large ‎error in the final decision. One of t...

Despite significant advances in risk management, routing hazardous materials (hazmat) has relied on relatively simpler methods. In this paper, we formally introduce an advanced risk measure, called conditional valueat-risk (CVaR), applied to truck routing problems for hazmat transportation. We find that CVaR offers a flexible, risk-averse, and computationally tractable routing method that is ad...