基于效用和均值-方差準(zhǔn)則的多人隨機(jī)微分博弈
發(fā)布時(shí)間:2019-02-19 09:25
【摘要】:以3人為例研究多人隨機(jī)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(duì)手——金融市場(chǎng).研究2種情形的隨機(jī)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(zhǔn)則的博弈.對(duì)于第一種情形,2個(gè)投資者的目標(biāo)是使終值財(cái)富的期望效用達(dá)到最大,金融市場(chǎng)的目標(biāo)是使該期望效用最小.對(duì)于第二種情形,2個(gè)投資者的目標(biāo)是在終值財(cái)富的期望給定時(shí)使終值財(cái)富的方差最小,金融市場(chǎng)的目標(biāo)是使方差最大.應(yīng)用隨機(jī)控制理論求得2個(gè)博弈問(wèn)題的最優(yōu)投資策略、最優(yōu)市場(chǎng)策略、最優(yōu)值函數(shù)的顯式解.通過(guò)研究,可以指導(dǎo)相互合作的兩投資者在金融市場(chǎng)情況惡劣時(shí),選擇恰當(dāng)?shù)耐顿Y策略使終值財(cái)富的期望效用最大,或使自身獲得一定的財(cái)富而面臨的風(fēng)險(xiǎn)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(xiàng)目(2016JM1024)
【分類號(hào)】:F830;O225
,
本文編號(hào):2426367
[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(xiàng)目(2016JM1024)
【分類號(hào)】:F830;O225
,
本文編號(hào):2426367
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