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Some Applications of Markov Additive Processes as Models in Insurance and Financial Mathematics.

机译：马尔可夫加法过程作为模型在保险和金融数学中的一些应用。

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摘要

This thesis consists mainly of three papers concerned with Markov additive processes, Lévy processes and applications on finance and insurance.;The first chapter is an introduction to Markov additive processes (MAP) and a presentation of the ruin problem and basic topics of Mathematical Finance. The second chapter contains the paper Lévy Systems and the Time Value of Ruin for Markov Additive Processes [7] written with Manuel Morales and that is published in the European Actuarial Journal. This paper studies the ruin problem for a Markov additive risk process. An expression of the expected discounted penalty function is obtained via identification of the Lévy systems. It is a generalization of results available in the literature for spectrally-negative Lévy risk processes and Markov-additive risk processes with phase-type jumps.;The third chapter contains the paper On a Generalization of the Expected Discounted Penalty Function to Include Deficits at and Beyond Ruin [6] that is submitted for publication. This paper presents an extension of the expected discounted penalty function in a setting involving aggregate claims modelled by a subordinator, and Brownian perturbation. This extension involves a sequence of expected discounted functions of successive minima reached by a jump of the risk process after ruin. It has important applications in risk management and in particular, it is used to compute the expected discounted value of capital injection.;Finally, the fourth chapter contains the paper The Minimal Entropy Martingale Measure (MEMM) for a Markov-Modulated Exponential Lévy Model [50] written with Romuald Hérvé Momeya and that is published in the journal Asia Pacific Financial Market . It presents new results related to the incompleteness problem in a financial market, where the risky asset is driven by Markov additive exponential model. These results characterize the martingale measure satisfying the entropy criterion. This measure is used to compute the price of the option and the portfolio of hedging in an exponential Markov-modulated Lévy model.;Key words: Minimal entropy martingale measure, exponential financial models, Markov additive processes, Lévy systems, ruin theory, Gerber-Shiu function, risk models.
机译：本论文主要包括三篇有关马尔可夫加法过程，Lévy过程及其在金融和保险中的应用的论文。第一章是马尔可夫加法过程（MAP）的介绍以及数学金融的破产问题和基本主题的介绍。第二章包含由曼努埃尔·莫拉莱斯（Manuel Morales）撰写的论文《列维系统和马尔可夫加法过程的废墟的时间价值》 [7]，该论文发表在《欧洲精算杂志》上。本文研究了马尔可夫加法风险过程的破产问题。预期的折现罚金函数的表达式是通过识别Lévy系统获得的。它是文献中针对频谱负Lévy风险过程和具有相位类型跳跃的马尔可夫加性风险过程的结果的概括。第三章包含论文“预期折现罚金函数的概括，以包括在和时的赤字”。提交出版的废墟[6]之外。本文介绍了在一个折价罚金函数的扩展情况，该函数涉及一个由下级建模的合计债权以及布朗扰动。此扩展涉及一系列破产后的风险过程跳跃所达到的一系列连续最小期望折现函数。它在风险管理中具有重要的应用，尤其是用于计算预期的注资贴现值。最后，第四章包含了论文的马尔可夫调制指数Lévy模型的最小熵Mar度量[MEMM] [ 50]由RomualdHérvéMomeya撰写，并发表在《亚太金融市场》杂志上。它提出了与金融市场中的不完全性问题有关的新结果，在该市场中，风险资产由马尔可夫加成指数模型驱动。这些结果表征了满足熵标准的mar测度。该度量用于在指数马尔可夫调制的Lévy模型中计算期权的价格和对冲组合。关键词：最小熵mar度量，指数金融模型，马尔可夫加法过程，Lévy系统，破产理论，Gerber- Shiu函数，风险模型。

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  • 作者

    Ben Salah, Zied.;

  • 作者单位

    Universite de Montreal (Canada).;

  • 授予单位 Universite de Montreal (Canada).;
  • 学科 Applied Mathematics.;Mathematics.
  • 学位 Ph.D.
  • 年度 2012
  • 页码 149 p.
  • 总页数 149
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 肿瘤学;
  • 关键词

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