15,443 research outputs found
Integrated asset liability modelling for property casuality insurance : a portfolio theoretical approach
In this paper we have developed a financial model of the non-life insurer to provide assistance for the management of the insurance company in making decisions on product, investment and reinsurance mix. The model is based on portfolio theory and recognizes the stochastic nature of and the interaction between the underwriting and investment income of the insurance business. In the context of an empirical application we illustrate howa portfolio optimisation approach can be used for asset-liability management
Joined-Up Pensions Policy in the UK: An Asset-Libility Model for Simultaneously Determining the Asset Allocation and Contribution Rate
The trustees of funded defined benefit pension schemes must make two vital and inter-related decisions - setting the asset allocation and the contribution rate. While these decisions are usually taken separately, it is argued that they are intimately related and should be taken jointly. The objective of funded pension schemes is taken to be the minimization of both the mean and the variance of the contribution rate, where the asset allocation decision is designed to achieve this objective. This is done by splitting the problem into two main steps. First, the Markowitz mean-variance model is generalised to include three types of pension scheme liabilities (actives, deferreds and pensioners), and this model is used to generate the efficient set of asset allocations. Second, for each point on the risk-return efficient set of the asset-liability portfolio model, the mathematical model of Haberman (1992) is used to compute the corresponding mean and variance of the contribution rate and funding ratio. Since the Haberman model assumes that the discount rate for computing the present value of liabilities equals the investment return, it is generalised to avoid this restriction. This generalisation removes the trade-off between contribution rate risk and funding ratio risk for a fixed spread period. Pension schemes need to choose a spread period, and it is shown how this can be set to minimise the variance of the contribution rate. Finally, using the result that the funding ratio follows an inverted gamma distribution, shortfall risk and expected tail loss are computed for funding below the minimum funding requirement, and funding above the taxation limit. This model is then applied to one of the largest UK pension schemes - the Universities Superannuation Scheme
Boosting insights in insurance tariff plans with tree-based machine learning methods
Pricing actuaries typically operate within the framework of generalized
linear models (GLMs). With the upswing of data analytics, our study puts focus
on machine learning methods to develop full tariff plans built from both the
frequency and severity of claims. We adapt the loss functions used in the
algorithms such that the specific characteristics of insurance data are
carefully incorporated: highly unbalanced count data with excess zeros and
varying exposure on the frequency side combined with scarce, but potentially
long-tailed data on the severity side. A key requirement is the need for
transparent and interpretable pricing models which are easily explainable to
all stakeholders. We therefore focus on machine learning with decision trees:
starting from simple regression trees, we work towards more advanced ensembles
such as random forests and boosted trees. We show how to choose the optimal
tuning parameters for these models in an elaborate cross-validation scheme, we
present visualization tools to obtain insights from the resulting models and
the economic value of these new modeling approaches is evaluated. Boosted trees
outperform the classical GLMs, allowing the insurer to form profitable
portfolios and to guard against potential adverse risk selection
Copulas in finance and insurance
Copulas provide a potential useful modeling tool to represent the dependence structure
among variables and to generate joint distributions by combining given marginal
distributions. Simulations play a relevant role in finance and insurance. They are used to
replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so
on. Using copulas, it is easy to construct and simulate from multivariate distributions based
on almost any choice of marginals and any type of dependence structure. In this paper we
outline recent contributions of statistical modeling using copulas in finance and insurance.
We review issues related to the notion of copulas, copula families, copula-based dynamic and
static dependence structure, copulas and latent factor models and simulation of copulas.
Finally, we outline hot topics in copulas with a special focus on model selection and
goodness-of-fit testing
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