【摘要】：以3人為例研究多人隨機微分博弈,其中2人為相互合作的投資者,另一人為2投資者博弈的"虛擬"對手——金融市場.研究2種情形的隨機微分博弈,一種情形為基于效用的博弈,另一種為基于均值-方差準則的博弈.對于第一種情形,2個投資者的目標是使終值財富的期望效用達到最大,金融市場的目標是使該期望效用最小.對于第二種情形,2個投資者的目標是在終值財富的期望給定時使終值財富的方差最小,金融市場的目標是使方差最大.應(yīng)用隨機控制理論求得2個博弈問題的最優(yōu)投資策略、最優(yōu)市場策略、最優(yōu)值函數(shù)的顯式解.通過研究,可以指導(dǎo)相互合作的兩投資者在金融市場情況惡劣時,選擇恰當?shù)耐顿Y策略使終值財富的期望效用最大,或使自身獲得一定的財富而面臨的風(fēng)險最小.
[Abstract]:Taking three people as an example, a multi-person stochastic differential game is studied, in which two are cooperative investors and the other is the "virtual" rival of the two-investor game, the financial market. The stochastic differential game of two cases is studied. One case is a game based on utility and the other is a game based on mean-variance criterion. In the first case, the goal of two investors is to maximize the expected utility of the final wealth, and the goal of the financial market is to minimize the expected utility. In the second case, the goal of the two investors is to minimize the variance of the final wealth when the expectation of the final wealth is given, and the goal of the financial market is to maximize the variance. By using stochastic control theory, the explicit solutions of the optimal investment strategy, optimal market strategy and optimal value function for two game problems are obtained. Through the research, we can guide the two investors who cooperate with each other to choose the appropriate investment strategy to maximize the expected utility of the final wealth or to obtain a certain amount of wealth and face the least risk when the financial market situation is bad.
【作者單位】： 西京學(xué)院理學(xué)院;
【基金】：陜西省自然科學(xué)基礎(chǔ)研究項目(2016JM1024)
【分類號】：F830;O225
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本文編號：2426367