论文标题
明确的föllmer-雪橇分解和离散化，并在指数lévy模型中进行跳跃校正
Explicit Föllmer--Schweizer decomposition and discretization with jump correction in exponential Lévy models
论文作者
论文摘要
我们研究了指数Lévy模型中的两个对冲问题。首先，我们为在轻度条件下的欧洲类型期权的Föllmer-Schweizer分解提供了明确的表示，这意味着相应的局部风险最小化策略的封闭式表达。其次，我们使用跳跃校正方法由指数lévy过程驱动的随机积分离散。随着预期的离散时间增加数量的增加，由加权BMO空间衡量了产生的离散误差的收敛率，这也意味着$ l_p $ - 估算值，$ p \ in（2，\ infty）$。此外，解决了满足反向Hölder不平等的措施的改变的影响。作为一种应用，研究了通过离散局部风险最小化策略引起的错误，以依赖莱维度量的性质，收益函数的规律性和所选的随机离散时间。
We investigate two hedging problems in exponential Lévy models. First, we provide an explicit representation for the Föllmer--Schweizer decomposition of European type options under mild conditions, which implies a closed-form expression of the corresponding local risk-minimizing strategies. Secondly, we discretize stochastic integrals driven by an exponential Lévy process using a jump correction method. The convergence rate of the resulting discretization error as the expected number of discretization times increases is measured in weighted BMO spaces, implying also $L_p$-estimates, $p \in (2, \infty)$. Moreover, the effect of a change of measure satisfying a reverse Hölder inequality is addressed. As an application, the error caused by discretizing the local risk-minimizing strategies is investigated in dependence of properties of the Lévy measure, the regularity of the payoff function and the chosen random discretization times.
