统计代写|生存模型代写survival model代考|ST227
如果你也在 怎样代写生存模型Survival Models这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。生存模型Survival Models在许多可用于分析事件时间数据的模型中，有4个是最突出的:Kaplan Meier模型、指数模型、Weibull模型和Cox比例风险模型。
生存模型Survival Models精算师和其他应用数学家使用预测人类或其他实体(有生命或无生命)生存模式的模型，并经常使用这些模型作为相当重要的财务计算的基础。具体来说，精算师使用这些模型来计算与个人人寿保险单、养老金计划和收入损失保险相关的财务价值。人口统计学家和其他社会科学家使用生存模型对该模型适用的人口的未来构成做出预测。
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统计代写|生存模型代写survival model代考|Use of Concomitant Variables
Intuitively, the distribution of strike durations may vary according to various characteristics of the labor group involved, such as (1) size of group, (2) type of industry, (3) time of year, (4) disputed issue(s), and (5) current state of the economy. As introduced in Section 8.5 , these concomitant variables can be represented in a parametric model fit to the data. In the case of the strike data, the first four of the influences listed above were taken into account by considering only data for which these variables were constant: $1000^{+}$size group, manufacturing industry, June strikes, and wage disputes.
In this section we expand our parametric model to include a concomitant variable addressing the general economic condition, an index of industrial production. We choose the Cox model given by Equation (8.77), with constant underlying hazard $\lambda=e^{a_0}$, and concomitant variable $z_1$ representing a fixed value of the index of industrial production associated with each strike. Then the hazard function is
$$
\lambda\left(t_j ; a_0, a_1, z_1\right)=e^{a_0+a_1 z_1},
$$
and the survival function is
$$
S\left(t_j ; a_0, a_1, z_1\right)=\exp \left[-t_j \cdot e^{a_0+a_1 z_1}\right]
$$
so the log-likelihood function, from Equation (11.16b), is
$$
\ell\left(a_0, a_1\right)=-\sum_{j=1}^n t_j \cdot e^{a_0+a_1 z_1}+\sum_{j=1}^n \delta_j\left(a_0+a_1 z_1\right) .
$$
统计代写|生存模型代写survival model代考|MORTGAGE LOAN PREPAYMENTS
In this section we will briefly explore the survival pattern of amortized loans, specifically those secured by a mortgage on real property. We assume that the actuarial reader is familiar with the mathematics of such loans, as described, for example, in Kellison [44].
When we speak of the survival pattern of an entity, there must be some definition of what it is that constitutes survival and, consequently, what constitutes lack of survival, or failure, of the entity. Consider a conventional mortgage loan of amount $L$, to be repaid over 30 years by 360 level monthly payments. If we were to define “survival” to be the continuation of the regular monthly payments, and “failure” to be the complete repayment of the loan, then the observed survival pattern, measured in months, for a loan that made all regular payments would be $S^{\circ}(t)=1.00$ for $0 \leq t<360$, and $S^{\circ}(360)=0$.
Most mortgage loans, however, do not behave with this pattern of perfect regularity, since there are two significant events that could occur to disturb it, namely default and prepayment. These two risks are discussed in Section 11.3.1. The major use of mortgage loan survival patterns is in conjunction with mortgage-backed securities (MBS), so an introduction to this investment instrument is presented in Section 11.3.2. Finally, in Section 11.3.3 we describe various models of mortgage loan survival in light of the default and prepayment risks that have, or have had, some use in the investment arena.
生存模型代考
统计代写|生存模型代写survival model代考|Use of Concomitant Variables
直观地说，罢工持续时间的分布可能根据所涉及的劳工群体的各种特征而变化，例如(1)群体规模，(2)行业类型，(3)一年中的时间，(4)有争议的问题，(5)当前的经济状况。正如第8.5节所介绍的，这些伴随变量可以用与数据拟合的参数模型来表示。在罢工数据的情况下，通过只考虑这些变量不变的数据，考虑了上面列出的前四个影响因素:$1000^{+}$规模集团、制造业、6月罢工和工资纠纷。
在本节中，我们将扩展我们的参数模型，以包括一个解决一般经济状况的伴随变量，即工业生产指数。我们选择由式(8.77)给出的Cox模型，其中潜在危险$\lambda=e^{a_0}$为常数，伴随变量$z_1$代表与每次罢工相关的工业生产指数的固定值。那么风险函数是
$$
\lambda\left(t_j ; a_0, a_1, z_1\right)=e^{a_0+a_1 z_1},
$$
生存函数是
$$
S\left(t_j ; a_0, a_1, z_1\right)=\exp \left[-t_j \cdot e^{a_0+a_1 z_1}\right]
$$
因此式(11.16b)的对数似然函数为
$$
\ell\left(a_0, a_1\right)=-\sum_{j=1}^n t_j \cdot e^{a_0+a_1 z_1}+\sum_{j=1}^n \delta_j\left(a_0+a_1 z_1\right) .
$$
统计代写|生存模型代写survival model代考|MORTGAGE LOAN PREPAYMENTS
在本节中，我们将简要探讨摊销贷款的生存模式，特别是那些由房地产抵押担保的贷款。我们假设精算读者熟悉此类贷款的数学计算，如Kellison[44]所描述的那样。
当我们谈到一个实体的生存模式时，必须对什么构成了生存，以及什么构成了实体的缺乏生存，或失败，有一个定义。考虑一笔数额为$L$的传统抵押贷款，将在30年内按360级每月付款偿还。如果我们将“生存”定义为每月定期还款的延续，而“失败”定义为贷款的完全偿还，那么观察到的生存模式，以月为单位衡量，对于所有定期还款的贷款，$0 \leq t<360$和$S^{\circ}(360)=0$的生存模式将是$S^{\circ}(t)=1.00$。
然而，大多数抵押贷款的行为并不符合这种完美的规律模式，因为有两个重大事件可能会扰乱它，即违约和提前还款。这两个风险将在第11.3.1节中讨论。抵押贷款生存模式的主要用途是与抵押贷款支持证券(MBS)结合使用，因此第11.3.2节介绍了这种投资工具。最后，在第11.3.3节中，我们根据已经或曾经在投资领域使用的违约和提前还款风险描述抵押贷款生存的各种模型。
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