光華講壇——社會(huì)名流與企業(yè)家論壇第6793期
主題：Optimal Stopping without Time Consistency時(shí)間非一致性下的最優(yōu)停止問(wèn)題
主講人：牛津大學(xué)數(shù)學(xué)研究所? 金含清副教授
主持人：數(shù)學(xué)學(xué)院院長(zhǎng) 馬敬堂教授
時(shí)間：9月18日16:00-17:00
地點(diǎn)：柳林校區(qū)通博樓B412會(huì)議室
主辦單位：數(shù)學(xué)學(xué)院 科研處
主講人簡(jiǎn)介：
金含清，博士，牛津大學(xué)副教授，牛津大學(xué)NIE金融大數(shù)據(jù)實(shí)驗(yàn)室主任。主要從事金融統(tǒng)計(jì)、金融數(shù)學(xué)、行為金融學(xué)等方面的研究，在Journal of Economic Theory、Mathematical Finance、SIAM Journal on Control and Optimization、Mathematics of Operations Research等Top期刊發(fā)表了數(shù)十篇高水平的論文，其中有多篇為被高引論文。擔(dān)任多個(gè)金融數(shù)學(xué)Top期刊的編委。
內(nèi)容提要：
In this work, we propose a new framework for solving a general dynamic optimal stopping problem without time consistency. A solution is proposed and is well-defined for any time setting and any form of objectives. A backward iteration is proposed to find the solution. The iteration works with some extra condition, which does not hold in general, but fortunately holds for the time inconsistency resulted by non-exponential discounting. When the iteration does not work, the equilibrium solution can be studied by a forward definition. The solution does not respect the widely-accepted backward induction solution (BIS) defined only for finite discrete time setting. On one hand, we find that our solution has some interesting property, which is missed by BIS. On the other hand, we proposed another solution inspired by the concept of rationalisability in game theory, which exists uniquely for general setting, and respects BIS in finite discrete time setting.
本講座提出了一個(gè)新的理論框架，用于求解具有普遍意義的時(shí)間非一致性下的最優(yōu)停止問(wèn)題。講座中所提出的解定義明確，適用于任意時(shí)間設(shè)置和任意形式的目標(biāo)函數(shù)，并提出了一種反向迭代算法以求解該問(wèn)題。該迭代算法的有效運(yùn)行需滿(mǎn)足特定附加條件——雖然該條件在一般情況下不成立，但幸運(yùn)的是它適用于由非指數(shù)貼現(xiàn)導(dǎo)致的時(shí)間不一致性情形。當(dāng)?shù)ㄊr(shí)，可以通過(guò)前向定義來(lái)研究均衡解。此解并不遵循目前被廣泛認(rèn)可的逆向歸納法（Backward Induction Solution, BIS）——需注意，逆向歸納法僅適用于有限離散時(shí)間設(shè)定。一方面，我們發(fā)現(xiàn)提出的解法具有逆向歸納法所不具備的若干有趣特性。另一方面，受博弈論中理性化概念的啟發(fā)，我們提出了另一種新解：該解在普遍設(shè)定下具有唯一存在性，且在有限離散時(shí)間設(shè)定下能夠與逆向歸納法保持一致性。
