时 间：2024年8 月14 日09:30-11:00
地 点：普陀校区理科大楼A1514
报告人：王若度 加拿大滑铁卢大学教授
主持人：李丹萍 华东师范大学教授
摘 要：
We analyze the problem of optimally sharing risk using allocations that exhibit counter-monotonicity, the most extreme form of negative dependence. Counter-monotonic allocations take the form of either ``winner-takes-all" lotteries or ``loser-loses-all" lotteries, and we respectively refer to these (normalized) cases as jackpot and scapegoat allocations. Our main theorem, the counter-monotonic improvement theorem, states that for a given set of random variables that are either all bounded from below or all bounded from above, one can always find a set of counter-monotonic random variables such that each component is greater or equal than its counterpart in the convex order. We show that Pareto optimal allocations, if they exist, must be jackpot allocations when all agents are risk seeking. We also consider the case of rank-dependent expected utility (RDU) agents and find conditions that guarantee that RDU agents prefer jackpot allocations. We provide an application for the mining of cryptocurrencies and show that in contrast to risk-averse miners, RDU miners with small computing power never join a mining pool. Finally, we characterize the competitive equilibria with risk-seeking agents, providing first and second fundamental theorems of welfare economics in this setting, where all equilibrium allocations are jackpot allocations.
报告人简介：
Dr. Ruodu Wang is Tier-1 Canada Research Chair in Quantitative Risk Management and Professor of Actuarial Science and Quantitative Finance at the University of Waterloo. He received his PhD in Mathematics (2012) from the Georgia Institute of Technology, after completing his Bachelor (2006) and Master’s (2009) degrees at Peking University. He serves on the board of 7 academic leading journals, including Operations Research, ASTIN Bulletin, European Actuarial Journal, and Mathematics of Operations Research. He is the first winner of the SOA Actuarial Science Early Career Award (2021) from the Society of Actuaries, and a Fellow of the Institute of Mathematical Statistics (elected 2022).