Recognizing that robust decision making is vital in risk management, this book provides concepts and algorithms for computing the best decision in view of the worstcase scenario. The main tool used is minimax, which ensures robust policies with guaranteed optimal performance that will improve further if the worst case is not realized. The applications considered are drawn from finance, but the design and algorithms presented are equally applicable to problems of economic policy, engineering design, and other areas of decision making. Critically, worstcase design addresses not only Armageddontype uncertainty. Indeed, the determination of the worst case becomes nontrivial when faced with numerous possibly infinite and reasonably likely rival scenarios. Optimality does not depend on any single scenario but on all the scenarios under consideration. Worstcase optimal decisions provide guaranteed optimal performance for systems operating within the specified scenario range indicating the uncertainty. The noninferiority of minimax solutions which also offer the possibility of multiple maxima ensures this optimality. Worstcase design is not intended to necessarily replace expected value optimization when the underlying uncertainty is stochastic. However, wise decision making requires the justification of policies based on expected value optimization in view of the worstcase scenario. Conversely, the cost of the assured performance provided by robust worstcase decision making needs to be evaluated relative to optimal expected values. Written for postgraduate students and researchers... See more
Recognizing that robust decision making is vital in risk management, this book provides concepts and algorithms for computing the best decision in view of the worstcase scenario. The main tool used is minimax, which ensures robust policies with guaranteed optimal performance that will improve further if the worst case is not realized. The applications considered are drawn from finance, but the design and algorithms presented are equally applicable to problems of economic policy, engineering design, and other areas of decision making. Critically, worstcase design addresses not only Armageddontype uncertainty. Indeed, the determination of the worst case becomes nontrivial when faced with numerous possibly infinite and reasonably likely rival scenarios. Optimality does not depend on any single scenario but on all the scenarios under consideration. Worstcase optimal decisions provide guaranteed optimal performance for systems operating within the specified scenario range indicating the uncertainty. The noninferiority of minimax solutions which also offer the possibility of multiple maxima ensures this optimality. Worstcase design is not intended to necessarily replace expected value optimization when the underlying uncertainty is stochastic. However, wise decision making requires the justification of policies based on expected value optimization in view of the worstcase scenario. Conversely, the cost of the assured performance provided by robust worstcase decision making needs to be evaluated relative to optimal expected values. Written for postgraduate students and researchers engaged in optimization, engineering design, economics, and finance, this book will also be invaluable to practitioners in risk management.
