A note on applications of stochastic ordering to control problems in insurance and finance

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2012-10-14 DOI:10.1080/17442508.2013.778861

N. Bäuerle, Erhan Bayraktar

引用次数: 22

Abstract

We consider a controlled diffusion process where the controller is allowed to choose drift and volatility from a set when . By choosing the largest at every point in time, an extremal process is constructed which is under suitable time changes stochastically larger than any other admissible process. This observation immediately leads to a very simple solution of problems where ruin or hitting probabilities have to be minimized. Under further conditions this extremal process also minimizes ‘drawdown’ probabilities.

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随机排序在保险和金融控制问题中的应用

我们考虑一个受控扩散过程，其中控制器允许从一组时间中选择漂移和波动。通过在每个时间点选择最大值，构造一个在适当的时间变化下随机大于其他任何允许过程的极值过程。这一观察结果立即引出了一个非常简单的问题解决方案，即必须最小化破坏或命中概率。在进一步的条件下，这种极端过程也使“收缩”概率最小化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.