6,106 research outputs found
Solvency capital, risk measures and comonotonicity: a review.
In this paper we examine and summarize properties of several well-known risk measures that can be used in the framework of setting solvency capital requirements for a risky business. Special attention is given to the class of (concave) distortion risk measures. We investigate the relationship between these risk measures and theories of choice under risk. Furthermore we consider the problem of how to evaluate risk measures for sums of non-independent random variables. Approximations for such sums, based on the concept of comonotonicity, are proposed. Several examples are provided to illustrate properties or to prove that certain properties do not hold. Although the paper contains several new results, it is written as an overview and pedagogical introduction to the subject of risk measurement. The paper is an extended version of Dhaene et al. (2003).Solvency; Risk; Risk measure; Comonotonicity; Framework; Requirements; Distortion risk measures; Theory; Choice; Random variables; Variables; Approximation; Risk measurement; Measurement;
Assessing Financial Model Risk
Model risk has a huge impact on any risk measurement procedure and its
quantification is therefore a crucial step. In this paper, we introduce three
quantitative measures of model risk when choosing a particular reference model
within a given class: the absolute measure of model risk, the relative measure
of model risk and the local measure of model risk. Each of the measures has a
specific purpose and so allows for flexibility. We illustrate the various
notions by studying some relevant examples, so as to emphasize the
practicability and tractability of our approach.Comment: 23 pages, 6 figure
Building Loss Models
This paper is intended as a guide to building insurance risk (loss) models. A typical model for insurance risk, the so-called collective risk model, treats the aggregate loss as having a compound distribution with two main components: one characterizing the arrival of claims and another describing the severity (or size) of loss resulting from the occurrence of a claim. In this paper we first present efficient simulation algorithms for several classes of claim arrival processes. Then we review a collection of loss distributions and present methods that can be used to assess the goodness-of-fit of the claim size distribution. The collective risk model is often used in health insurance and in general insurance, whenever the main risk components are the number of insurance claims and the amount of the claims. It can also be used for modeling other non-insurance product risks, such as credit and operational risk.Insurance risk model; Loss distribution; Claim arrival process; Poisson process; Renewal process; Random variable generation; Goodness-of-fit testing
Online Predictive Optimization Framework for Stochastic Demand-Responsive Transit Services
This study develops an online predictive optimization framework for
dynamically operating a transit service in an area of crowd movements. The
proposed framework integrates demand prediction and supply optimization to
periodically redesign the service routes based on recently observed demand. To
predict demand for the service, we use Quantile Regression to estimate the
marginal distribution of movement counts between each pair of serviced
locations. The framework then combines these marginals into a joint demand
distribution by constructing a Gaussian copula, which captures the structure of
correlation between the marginals. For supply optimization, we devise a linear
programming model, which simultaneously determines the route structure and the
service frequency according to the predicted demand. Importantly, our framework
both preserves the uncertainty structure of future demand and leverages this
for robust route optimization, while keeping both components decoupled. We
evaluate our framework using a real-world case study of autonomous mobility in
a university campus in Denmark. The results show that our framework often
obtains the ground truth optimal solution, and can outperform conventional
methods for route optimization, which do not leverage full predictive
distributions.Comment: 34 pages, 12 figures, 5 table
Optimal stopping under probability distortion
We formulate an optimal stopping problem for a geometric Brownian motion
where the probability scale is distorted by a general nonlinear function. The
problem is inherently time inconsistent due to the Choquet integration
involved. We develop a new approach, based on a reformulation of the problem
where one optimally chooses the probability distribution or quantile function
of the stopped state. An optimal stopping time can then be recovered from the
obtained distribution/quantile function, either in a straightforward way for
several important cases or in general via the Skorokhod embedding. This
approach enables us to solve the problem in a fairly general manner with
different shapes of the payoff and probability distortion functions. We also
discuss economical interpretations of the results. In particular, we justify
several liquidation strategies widely adopted in stock trading, including those
of "buy and hold", "cut loss or take profit", "cut loss and let profit run" and
"sell on a percentage of historical high".Comment: Published in at http://dx.doi.org/10.1214/11-AAP838 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Building Loss Models
This paper is intended as a guide to building insurance risk (loss) models. A typical model for insurance risk, the so-called collective risk model, treats the aggregate loss as having a compound distribution with two main components: one characterizing the arrival of claims and another describing the severity (or size) of loss resulting from the occurrence of a claim. In this paper we first present efficient simulation algorithms for several classes of claim arrival processes. Then we review a collection of loss distributions and present methods that can be used to assess the goodness-of-fit of the claim size distribution. The collective risk model is often used in health insurance and in general insurance, whenever the main risk components are the number of insurance claims and the amount of the claims. It can also be used for modeling other non-insurance product risks, such as credit and operational risk.Insurance risk model; Loss distribution; Claim arrival process; Poisson process; Renewal process; Random variable generation; Goodness-of-fit testing;
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