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Mean-Variance Hedging Based on an Incomplete Market with External Risk Factors of Non- Gaussian OU Processes

机译：基于具有非高斯OU过程外部风险因素的不完整市场的均值方差套期

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摘要

We prove the global risk optimality of the hedging strategy of contingent claim, which is explicitly (or called semiexplicitly) constructed for an incomplete financial market with external risk factors of non-Gaussian Ornstein-Uhlenbeck (NGOU) processes. Analytical and numerical examples are both presented to illustrate the effectiveness of our optimal strategy. Our study establishes the connection between our financial system and existing general semimartingale based discussions by justifying required conditions. More precisely, there are three steps involved. First, we firmly prove the no-arbitrage condition to be true for our financial market, which is used as an assumption in existing discussions. In doing so, we explicitly construct the square-integrable density process of the variance-optimal martingale measure (VOMM). Second, we derive a backward stochastic differential equation (BSDE) with jumps for the mean-value process of a given contingent claim. The unique existence of adapted strong solution to the BSDE is proved under suitable terminal conditions including both European call and put options as special cases. Third, by combining the solution of the BSDE and the VOMM, we reach the justification of the global risk optimality for our hedging strategy.
机译：我们证明了或有债权对冲策略的全局风险最优性，它是针对具有非高斯Ornstein-Uhlenbeck（NGOU）流程外部风险因素的不完整金融市场而明确（或半隐式）构造的。给出了分析和数值示例，以说明我们最佳策略的有效性。我们的研究通过证明所需条件的合理性，建立了我们的金融系统与现有的基于一般半市场的讨论之间的联系。更准确地说，涉及三个步骤。首先，我们坚决证明无套利条件适用于我们的金融市场，在现有讨论中将其用作假设。在此过程中，我们显式构造了方差最优mar测度（VOMM）的平方可积密度过程。其次，对于给定的或有债权的均值过程，我们导出了具有跳跃的后向随机微分方程（BSDE）。在适当的终端条件下（包括欧洲看涨期权和看跌期权作为特殊情况），证明了针对BSDE的强大解决方案的独特存在。第三，通过结合BSDE和VOMM的解决方案，我们得出了对冲策略的全球风险最优性的理由。

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  • 来源
    《Mathematical Problems in Engineering》 |2015年第6期|625289.1-625289.20|共20页
  • 作者

    Dai Wanyang;

  • 作者单位

    Nanjing Univ, State Key Lab Novel Software Technol, Nanjing 210093, Jiangsu, Peoples R China.;

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