论文标题
在不完整的跳跃扩散市场中的欧洲选择定价
Pricing of European options in incomplete jump diffusion markets
论文作者
论文摘要
我们在金融市场上研究风险资产价格以跳跃扩散为模型的期权价格。 Schweizer（1996）在一般的Semimartingale环境中提出，此前Föllmerand Sondermann（1986）和Bouleau和Bouleau and Lamberton（1989）提出了这种选择的最初财富，即可通过自我融合投资组合产生的最初财富所需的最初财富，这是可以自给自足的，从而使付费的差异很大，这是可能的。 Schweizer称此价格为近似价格，他调查了该价格的有趣一般性及其相应的最佳投资组合。 - 但是，在具体情况下，这些作者都没有明确计算这个价格。这是当前论文的动机：我们使用随机控制方法在市场上以跳投扩散描述的资产来计算这个价格。我们的方法涉及Stackelberg游戏和适当修改的随机最大原理。 我们表明，具有Z^表示的最佳初始财富，存在相应的最佳投资组合π^，并且是唯一的。 - 如果风险资产价格的系数是确定性的，我们表明z^= e_ {q*} [f]，对于特定的同等标准级量度（EMM）q*。这特别表明，最小的差异价格不受套利。 -Then for the general case we apply a suitable maximum principle of optimal stochastic control to relate the minimal variance price z^=p_{mv}(F) to the Hamiltonian and its adjoint processes, and we show that, under some conditions, z^=E_{Q_0}[F] for any Q_0 in a family M_0 of EMMs, described by the set of solutions of a system of linear equations. - 最终，我们通过查看特定示例来说明结果。
We study option prices in financial markets where the risky asset prices are modelled by jump diffusions. It was proposed by Schweizer (1996) in a general semimartingale setting, following earlier works by Föllmer and Sondermann (1986) and Bouleau and Lamberton (1989), that the right price of such an option is the initial wealth needed to make it possible to generate by a self-financing portfolio a terminal wealth which is as close as possible to the payoff F in the sense of variance. Schweizer calls this price the approximation price and he investigates interesting general properties of this price and its corresponding optimal portfolio. -However, neither of these authors compute explicitly this price in concrete cases. This is the motivation for the current paper: We apply stochastic control methods to compute this price in the setting of markets with assets described by jump diffusions. Our method involves Stackelberg games and a suitably modified stochastic maximum principle. We show that such an optimal initial wealth, denoted by z^, with corresponding optimal portfolio π^ exist and are unique. - If the coefficients of the risky asset prices are deterministic, we show that z^=E_{Q*}[F], for a specific equivalent martingale measure (EMM) Q*. This shows in particular that the minimal variance price is free from arbitrage. -Then for the general case we apply a suitable maximum principle of optimal stochastic control to relate the minimal variance price z^=p_{mv}(F) to the Hamiltonian and its adjoint processes, and we show that, under some conditions, z^=E_{Q_0}[F] for any Q_0 in a family M_0 of EMMs, described by the set of solutions of a system of linear equations. -Finally, we illustrate our results by looking at specific examples.
