Stochastic quasi-gradient techniques in VaR-based ALM models (Q2740085)

This paper deals with the minimization problem for Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). Let us denote by \(f(x,r(\theta))\) the function of losses in a portfolio value which depends on the decision vector \(x\) and the random parameter vector \(r(\theta)\) and let be \(\Phi(x,L)\) the probability that losses will not exceed \(L\): \(\Phi(x,L)=\int_{r:f(x,r)\leq L}p(r) dr\). VaR and CVaR could be defined respectively as \(VaR(x,\alpha)=\min\{L:\Phi(x,L)\geq\alpha\}\), NEWLINE\[NEWLINECVaR(x,\alpha)=(1-\alpha)^{-1}\int_{r:f(x,r)\geq VaR(x,\alpha)}f(x,r)p(r) dr.NEWLINE\]NEWLINE The author demonstrates the possibility of using quasi-gradient techniques in VaR-based asset-liability management optimization models. The proposed approach was used for the real-life asset-liability management problem, namely the management of the inter-bank loans portfolio of the commercial bank.