Optimal portfolios when stock prices follow an exponential Lévy process
Optimal portfolios when stock prices follow an exponential Lévy process
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DOI：
10.1007/s00780-003-0105-4
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发表时间：
2004
影响因子：
1.7
通讯作者：
Susanne Emmer;C. Klüppelberg
中科院分区：
文献类型：
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作者：
Susanne Emmer;C. Klüppelberg
我们研究了一些投资组合问题，这些问题包括在风险上界的约束下最大化期望终端财富，其中我们用方差来衡量风险，同时也用在险资本(CAR)来衡量风险。对于任何服从指数L过程的价格过程，均值-方差问题的解都具有相同的结构。这辆车涉及投资组合相应财富过程的一个分位数。我们用一个较简单的Lévy过程，通常是漂移项、布朗运动和复合泊松过程的和，得到了它的一个弱极限律。研究了L过程与其随机指数之间的某些关系。
We investigate some portfolio problems that consist of maximizing expected terminal wealth under the constraint of an upper bound for the risk, where we measure risk by the variance, but also by the Capital-at-Risk (CaR). The solution of the mean-variance problem has the same structure for any price process which follows an exponential Lévy process. The CaR involves a quantile of the corresponding wealth process of the portfolio. We derive a weak limit law for its approximation by a simpler Lévy process, often the sum of a drift term, a Brownian motion and a compound Poisson process. Certain relations between a Lévy process and its stochastic exponential are investigated.