### 统计代写|金融中的随机方法作业代写Stochastic Methods in Finance代考| Dynamic Portfolio Management for Property

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|金融中的随机方法作业代写Stochastic Methods in Finance代考|Casualty Insurance

Increasing competition in the insurance sector in developed countries, and more recently record property and casualty $(\mathrm{P \& C}$ ) insurance claims reported by global players (CEA, 2010; Europe Economics, 2010), has gencrated remarkable

pressures on the financial stability of $\mathrm{P} \& \mathrm{C}$ divisions within insurance firms, leading to increased technical reserves and requiring a higher capital base (European Parliament, 2009). At the same time we have witnessed a remarkable expansion of investment management divisions, reinforcing the role of insurers as institutional investors competing in fixed income and equity markets with other players such as pension and mutual funds. Increasing market volatility in the last few years has, as a result, affected large insurers’ market risk exposure. Regulatory bodies, through the Solvency II regulation (European Parliament, 2009; ISVAP, 2010), have supported risk-based capital allocation measures for insurance firms as a whole. As a response large insurance companies have pursued restructuring aimed from an operational perspective at integrating the historical insurance business with the investment management business. Such an integration is also motivated by the perceived role of the $\mathrm{P} \& \mathrm{C}$ division as a liquidity buffer for the cash deficits generated by fixed income portfolios typically held by risk-averse investment divisions. A trade-off between safe liquidity conditions, key to shareholders’ short-mediumterm returns, and long-term business sustainability has emerged and lead to strategies based on long-term horizons. This motivates the adoption of a multistage stochastic programming (MSP) problem formulation (Birge and Louveaux, 1997; Cariño et al., 1994; Consigli and Dempster, 1998; Mulvey and Erkan, 2005; Zenios and Ziemba, 2007a) able to capture both short- and long-term goals. Contrary to current standards in insurance-based investment divisions which largely rely on one-period static approaches (de Lange et al., 2003; Mulvey and Erkan, 2003; Zenios and Ziemba, 2007b), the adoption of dynamic approaches allows both the extension of the decision horizon and a more accurate short-term modelling of $P \& C$ variables.

In this chapter we present an asset-liability management (ALM) problem integrating the definition of an optimal asset allocation policy over a 10-year planning horizon with the inclusion of liability constraints generated by an ongoing P\&C business (de Lange et al., 2003; Dempster et al., 2003; Mulvey and Erkan, 2005; Mulvey et al., 2007). Relying on a simplified P\&C income statement we clarify the interaction between the investment and the classical insurance business and introduce an objective function capturing short-, medium-, and long-term goals within a multistage model. The planning horizon is divided in six time periods: four quarters in the first year and then 2 and 7 years to reach the 10 -year horizon. Over this period alternative insurance and financial scenarios will affect the insurance management optimal forward policy. We show that integrated management of the insurance liability and asset portfolios is required to protect firm solvency in the presence of unexpectedly increased P\&C claims. A relatively simple multivariate Gaussian return model is adopted to generate return scenarios (Dupačová et al., 2001) for a realistic investment universe including fixed income, equity, and real estate investment opportunities.

## 统计代写|金融中的随机方法作业代写Stochastic Methods in Finance代考|P&C Income Generation and Asset Allocation

We consider an insurance company holding a property and casualty liability portfolio with annual issuance of insurance contracts and a diversified asset portfolio spanning fixed income, real estate, and equity markets. The insurance management sets a target for the end-of-the-year operating profit on an annual basis and seeks an optimal trade-off between this short-term goal, medium-term industrial plan targets, and a (10-year) long-term sustainability goal. The company’s financial soundness will depend on the solidity of both the $\mathrm{P} \& \mathrm{C}$ business division, hereafter also referred to as the technical division, and the imvestment division. In a simplified framework, with stable insurance provisions and reserves, we assume that technical profitability primarily depends on collected annual premiums, operating and human resource costs, and, crucially, recorded insurance claims. We assume throughout that the company will fix insurance premiums so as to maintain its market position within a highly competitive market and that the operational efficiency with minimal operating, staff and administrative costs is maintained over time exogenously to the optimal financial management problem. In this setting alternative insurance claim scenarios are likely from 1 year to the next to heavily affect the company technical profitability. Increasing technical provisions may, on the other hand, weaken the capital base. This is indeed the risk faced currently by several global players in the insurance sector (Europe Economics, 2010), with record claims in the automotive and increasingly the real estate sector, and regarding catastrophic events (CAT risk events). Under such conditions the management will search for an asset portfolio strategy able to preserve the firm’s liquidity in the short term and its overall sustainability in the long term. Only the first goal ean be aecommodated within

a static 1-year decision problem. The investment profit depends on realized price gains from trading, dividends, and interest cash flows generated by the asset portfolio; see Table 5.1. Risky investment strategies may very well generate sufficient liquidity and financial profit over I year but then lead to heavy long-term losses, jeopardizing the company’s market position and solvency. Revenues and costs, as shown in Table $5.1$, will affect annually the firm’s profitability and are considered in the ALM model formulation.

The P\&C annual operating profit does not consider the portfolio’s gain and losses, which, if unrealized, reflect the asset portfolio’s revaluation over time (and can translate into current realized gains or losses if required). If actually realized portfolio profits and losses are nevertheless considered outside the core insurance activity. Net of future liabilities, the maximization of the investment portfolio expected value, can thus be considered a medium-term goal to be pursued by the management. Realized investment and technical profits, together with unrealized gains, will eventually jointly determine the business long-term sustainability reflected in the 10-year target. We assume a 10-year decision horizon with the first year divided into four quarters, a subsequent 2 -year stage and a final 7 -year stage as shown in Fig. 5.1.

## 统计代写|金融中的随机方法作业代写Stochastic Methods in Finance代考|Asset–Liability Management for P&C Companies

A generic P\&C ALM problem relies on the specification by the insurance firm’s actuarial division of the reserves and expected cash flows from premiums and insurance claims. In a multistage approach such inputs provide a first-year average scenario to depart from in order to assess, assuming ongoing business, the effects of these departures on longer term technical scenarios and to find an optimal asset management strategy under exogenous liquidity constraints. This set of scenario-dependent variables reflects the uncertainty faced by management in a dynamic framework. As shown in Fig. $5.1$ the initial model decision at time $t=0$ is the only one taken under full uncertainty, while subsequent decisions will all depend on previous decisions and future residual uncertainty. Such uncertainty is modelled through a scenario tree (Consigli et al., 2010; Dupačová et al., 2001; Kouwenberg, 2001; Pflug and Römisch, 2007) such as the one shown schematically in Fig. 5.3: every path, from the root node to a leaf node at the 10 -year horizon represents a scenario.

The stochastic programming formulation relies on the specification of the underlying random factors as tree processes endowed with a given branching structure. In the formulation of the ALM problem we denote by $R(t, s)$ the insurance premiums collected in stage $t$ under scenario $s$. Premiums represent the fundamental cash flows generated every year by the technical business. For given P\&C contract renewals, the insurance actuarial division will periodically revise its estimate on forthcoming claims $L(t, s)$ and required statutory and discretional reserves $\Lambda(t, s)$. These quantities for given human resources and administrative costs $C(t, s)$ will determine the behaviour of the company’s combined ratio: this is the ratio of all insurance

claims and technical costs to the earned premiums. A bad liability scenario will thus be associated with increasing insurance claims at a time of reducing premium renewals and operational inefficiency. Consequently the ex post combined ratio will increase and may go over the $100 \%$ threshold. The firm’s investment profit, instead, is generated by realized capital gains $G(t, s)$ in stage $t$, scenario $s$; the interest margin, defined as the difference between positive and negative interest cash flows, $M(t, s)=I^{+}(t, s)-I^{-}(t, s)$; and by dividends $D(t, s)$ and other financial revenues $Y(t, s)$.

The annual income $\Pi(t, s)$ is determined by the sum of technical and investment profit. The net income, here assumed entirely distributed, is derived by subtracting the corporate tax $T$ from the profit $D^{-}(t, s)=\Pi(t, s)(1-T)$.

## 统计代写|金融中的随机方法作业代写Stochastic Methods in Finance代考|P&C Income Generation and Asset Allocation

P\&C 年度营业利润不考虑投资组合的损益，如果未实现，则反映资产组合随时间的重估（如果需要，可以转化为当前已实现的损益）。如果实际实现的投资组合利润和损失仍然被视为核心保险活动之外。因此，扣除未来负债后，投资组合预期价值的最大化可以被视为管理层追求的中期目标。已实现的投资和技术利润，以及未实现的收益，最终将共同决定10年目标所体现的业务长期可持续性。我们假设一个 10 年的决策期限，第一年分为四个季度，随后是 2 年阶段和最后 7 年阶段，如图 5.1 所示。

## 广义线性模型代考

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。