Risk minimizing portfolios and HJBI equations for stochastic differential games
Risk minimizing portfolios and HJBI equations for stochastic differential games
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DOI：
10.1080/17442500701655408
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发表时间：
2008-01-01
影响因子：
0.9
通讯作者：
Oksendal, Bernt
中科院分区：
文献类型：
--
作者：
Mataramvura, Sure;Oksendal, Bernt
本文研究了在跳跃扩散市场中寻找一个最小化终端财富凸风险测度的市场投资组合问题。我们制定的问题作为一个两个球员（零和）随机微分游戏。为了帮助我们找到一个解决方案，我们证明了一个定理，给出了一般的零和随机微分对策在跳跃扩散设置的Hamilton-Jacobi-Bellman-Isaacs（HJBI）条件。然后，我们使用该定理来研究特定的风险最小化问题。最后，我们扩展我们的方法，以涵盖一般的随机微分游戏（不一定是零和），我们得到类似的HJBI方程的纳什均衡这样的游戏。
In this paper, we consider the problem to find a market portfolio that minimizes the convex risk measure of the terminal wealth in a jump diffusion market. We formulate the problem as a two player (zero-sum) stochastic differential game. To help us find a solution, we prove a theorem giving the Hamilton-Jacobi-Bellman-Isaacs (HJBI) conditions for a general zero-sum stochastic differential game in a jump diffusion setting. We then use the theorem to study particular risk minimization problems. Finally, we extend our approach to cover general stochastic differential games (not necessarily zero-sum), and we obtain similar HJBI equations for the Nash equilibria of such games.