The Mathematics and Statistics of Quantitative Risk Management

It was the aim of this workshop to gather a multidisciplinary and international group of scientists at the forefront of research in areas related to the mathematics and statistics of quantitative risk management. The main objectives of this workshop were to break down disciplinary barriers that often limit collaborative research in quantitative risk management, and to communicate the state of the art research from the different disciplines, and to point towards new directions of research

A worst-case optimization approach to impulse perturbed stochastic control with application to financial risk management

This work presents the main ideas, methods and results of the theory of impulse perturbed stochastic control as an extension of the classic stochastic control theory. Apart from the introduction and the motivation of the basic concept, two stochastic optimization problems are the focus of the investigations. On the one hand we consider a differential game as analogue of the expected utility maximization problem in the situation with impulse perturbation, and on the other hand we study an appropriate version of a target problem. By dynamic optimization principles we characterize the associated value functions by systems of partial differential equations (PDEs). More precisely, we deal with variational inequalities whose single inequalities comprise constrained optimization problems, where the corresponding admissibility sets again are given by the seeked value functions. Using the concept of viscosity solutions as weak solutions of PDEs, we avoid strong regularity assumptions on the value functions. To use this concept as sufficient verification method, we additionally have to prove the uniqueness of the solutions of the PDEs. As a second major part of this work we apply the presented theory of impulse perturbed stochastic control in the field of financial risk management where extreme events have to be taken into account in order to control risks in a reasonable way. Such extreme scenarios are modelled by impulse controls and the financial decisions are made with respect to the worstcase scenario. In a first example we discuss portfolio problems as well as pricing problems on a capital market with crash risk. In particular, we consider the possibility of trading options and study their in uence on the investor's performance measured by the expected utility of terminal wealth. This brings up the question of crash-adjusted option prices and leads to the introduction of crash insurance. The second application concerns an insurance company which faces potentially large losses from extreme damages. We propose a dynamic model where the insurance company controls its risk process by reinsurance in form of proportional reinsurance and catastrophe reinsurance. Optimal reinsurance strategies are obtained by maximizing expected utility of the terminal surplus value and by minimizing the required capital reserves associated to the risk process

The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

Recent Developments in Financial and Insurance Mathematics and the Interplay with the Industry

The workshop brought together leading experts from all over the world to exchange and discuss the latest developments in mathematical finance and actuarial mathematics. Researchers from the industry had the opportunity to circulate their problems among mathematicians. The participants gained from a fruitful interaction between mathematical methods and practitioner’s problems as well as from the interaction between finance and actuarial mathematics

Essays on Risk Pricing in Insurance

Pricing risks in the insurance business is an essential task for actuaries. Implementing the appropriate pricing techniques to improve risk management and optimize its financial gain requires a thorough understanding of underlying risks and their interactions. In this dissertation, I address risk pricing in the context of insurance company by reviewing methods applied in practice, proposing new models, and also exploring different aspects of insurance risks. This dissertation consists of three chapters. The first chapter provides a survey of existing capital allocation methods, including common approaches based on the gradients of risk measures and “economic” allocation arising from counterparty risk aversion. All methods are implemented in two example settings: binomial losses and using loss realizations from a catastrophe reinsurer. The stability of allocations is assessed based on sensitivity analysis with regards to losses. The results show that capital allocations appear to be intrinsically (geometrically) related, although the stability varies considerably. Stark differences exist between common and “economic” capital allocations. The second chapter develops a dynamic profit maximization model for a financial institution with liabilities of varying maturity, and uses it for determining the term structure of capital costs. iii As a key contribution, the theoretical, numerical, and empirical results show that liabilities with different terms are assessed differently, depending on the company’s financial situation. In particular, for a financially constrained firm, value-adjustments due to financial frictions for liabilities in the far future are less pronounced than for short-term obligations, resulting in a strongly downward sloping term structure. The findings provide guidance for performance measurement in financial institutions. The third chapter estimates a flexible affine stochastic mortality model based on a set of US term life insurance prices using a generalized method of moments approach to infer forward-looking, market-based mortality trends. The results show that neither mortality shocks nor stochasticity in the aggregate trend seem to affect the prices. In contrast, allowing for heterogeneity in the mortality rates across carriers is crucial. The major conclusion is that for life insurance, rather than aggregate mortality risk, the key risks emanate from the composition of the portfolio of policyholders. These findings have consequences for mortality risk management and emphasize important directions of mortality-related actuarial research

Cooperative Game Theory and its Insurance Applications

This survey paper presents the basic concepts of cooperative game theory, at an elementary level. Five examples, including three insurance applications, are progressively developed throughout the paper. The characteristic function, the core, the stable sets, the Shapley value, the Nash and Kalai-Smorodinsky solutions are defined and computed for the different examples

Risk measure changes and portfolio optimization theory

Imperial Users onl