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On Kusuoka representation of law invariant risk measures

Shapiro, Alexander - In: Mathematics of operations research 38 (2013) 1, pp. 142-152

Persistent link: https://www.econbiz.de/10009727684

Tutorial on risk neutral, distributionally robust and risk averse multistage stochastic programming

Shapiro, Alexander - In: European journal of operational research : EJOR 288 (2021) 1, pp. 1-13

Persistent link: https://www.econbiz.de/10012496519

Bounds for nested law invariant coherent risk measures

Xin, Linwei; Shapiro, Alexander - In: Operations research letters 40 (2012) 6, pp. 431-435

Persistent link: https://www.econbiz.de/10009716584

Risk neutral and risk averse approaches to multistage renewable investment planning under uncertainty

Bruno, Sergio; Ahmed, Shabbir; Shapiro, Alexander; … - In: European journal of operational research : EJOR 250 (2016) 3, pp. 979-989

Persistent link: https://www.econbiz.de/10011445359

Risk neutral and risk averse Stochastic Dual Dynamic Programming method

Shapiro, Alexander; Tekaya, Wajdi; Costa, Joari Paulo da; … - In: European journal of operational research : EJOR 224 (2013) 2, pp. 375-391

Persistent link: https://www.econbiz.de/10009683060

Risk neutral reformulation approach to risk averse stochastic programming

Liu, Rui Peng; Shapiro, Alexander - In: European journal of operational research : EJOR 286 (2020) 1, pp. 21-31

Persistent link: https://www.econbiz.de/10012239878

Conditional Risk Mappings

Ruszczynski, Andrzej; Shapiro, Alexander - EconWPA - 2004

We introduce an axiomatic definition of a conditional convex risk mapping. By employing the techniques of conjugate duality we derive properties of conditional risk mappings. In particular, we prove a representation theorem for conditional risk mappings in terms of conditional expectations. We...

Persistent link: https://www.econbiz.de/10005561062