Informational markets: Risk modelling, risk management and portfolio analysis

信息市场：风险建模、风险管理和投资组合分析

• 批准号: RGPIN-2019-04779
• 负责人: Choulli, Tahir
• 金额: $ 1.31万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=758335
• 关键词: Informational; markets; Risk; modelling; risk

An informational market is a market where there are two flows of information. One flow denoted by F represents the ``public" information, which is available to all agents, and a larger flow G that contains F and additional information about events that might affect the market. Thus, our starting point in this project is the initial market model described by the pair (S,F), to which we add several random times. Here S represents the stocks' price process and F is the filtration that models the ``public" of information. The random times can model the death times of insured agents for life insurance, or the defaults times of firms for credit risk theory, or more generally the occurrence times of events that might impact the market. Given that death times can not be seen before they occur, the progressively enlargement approach for modelling the connection between F, G and the random times, seems tailored-fit for these aforementioned domains. In this setting, our main objectives reside in understanding the different types of risks induced by the uncertainties in the random times alone and/or jointly with the filtration F. Precisely, we are interested in answering the following questions: Can we single out the risk(s) that can be classified as ``pure random times' risk"? How many are there of such risk(s)? How these risk(s) interplay with the risk(s) coming from the initial market (S,F)? Above all, can we define a risk-basis for the larger flow G, and every risk with respect to this filtration can be decomposed uniquely with respect to this basis? Via detailed answers to these questions, we will deeply understand how risks build up as soon as we add more uncertainties to a model, we provide a cutting- edge mathematical modelling and quantification for the risk. This will allow us to efficiently design risk management tools afterwards. Besides these, the projected applications of our study are numerous and multifold. First of all, we will be able to tell fully how far the additional uncertainties affect the fundamental financial and/or economic concepts of arbitrage theory and market's viability that are intimately related to market's liquidity. Furthermore, when these concepts fail for (S,G), we should be able to suggest market's regulation(s) policies in order to repair the damage induced by the ``extra" information. Secondly, we want to describe the dynamics and the stochastic structures for mortality and/or longevity derivatives, such as longevity bonds, which are highly important for the mortality/longevity securitization. We are also interested in describing completely and fully the set of all deflators under G, which is interesting in itself besides its vital role in the portfolio analysis. Finally, we are will investigate the impact of the random times on optimal portfolios (for various optimization criterion), the numeraire portfolio, and on the existing pricing rules as well.

信息市场是一个有两个信息流的市场。 F表示``公开''信息，该信息可用于所有代理商，并且包含F的较大流动g以及有关可能影响市场的事件的其他信息。因此，我们在该项目中的起点是该项目所描述的初始市场模型（s，f），我们在此添加了几个随机时间。在这里添加了几个股票的价格。随机时间可以为被保险人的人寿保险的死亡时间建模，或者是企业的信用风险理论的默认时间，或者更一般而言，可能会影响市场的事件的发生时间。鉴于死亡时间在发生之前无法看见，因此，用于建模F，G和随机时间之间的连接的逐渐扩大方法似乎是针对这些上述域而量身定制的。在这种情况下，我们的主要目标是理解仅随机时间和/或与过滤F的不确定性引起的不同类型的风险。确切地说，我们有兴趣回答以下问题：我们可以挑出风险（s）可以分类为``纯随机时间''风险的风险。 （s，F）最重要的是，我们可以通过对这些问题的详细答案来定义更大的流动g，而对此，我们将在对这些模型中添加更高的模型，以使我们更加了解这些模型我们的研究的预计应用是多数的。 Furthermore, when these concepts fail for (S,G), we should be able to suggest market's regulation(s) policies in order to repair the damage induced by the ``extra" information. Secondly, we want to describe the dynamics and the stochastic structures for mortality and/or longevity derivatives, such as longevity bonds, which are highly important for the mortality/longevity securitization. We are also interested in describing completely and fully G下的所有缩水器的集合本身在投资组合分析中的重要作用外，我们将研究随机时间对最佳投资组合的影响（用于各种优化标准），Numeraire Portfolio以及对现有定价规则的影响。