This has often resulted in common open issues and has induced a remarkable effort by the industrial and scientific communities to facilitate the adoption of advanced analytical and decision tools. Salzmann and Wüthrich 2010 , Moehr 2011 , Wüthrich and Merz 2013 and Pelsser and Stadje 2014. However to price insurance liabilities it is not sufficient to consider expected insurance liabilities. Third, given the long-term nature of many insurance liabilities, it is not clear what a multi-period extension of cost-of-capital valuation principles should be. We set up a general framework for the cost-of-capital margin and relate it to dynamic risk measurement. We start off by discussing model and, in particular, parameter uncertainty. Typically, two- or three-factor versions allow to capture the dependence structure between yields with different times to maturity in an appropriate way.
The first half of the book focuses on general methods, whereas the second half discusses model-specific algorithms. In this book we define a comprehensive mathematical framework that adequately describes price formation and captures the corresponding risk factors that influence the stability of the financial industry. Describing the latest advances in the field, Quantitative Risk Management covers the methods for market, credit and operational risk modelling. This will result in the split of the filtration into a financial filtration and an insurance technical filtration which describe the corresponding flow of information. In this paper we study the hedging of typical life insurance payment processes in a general setting by means of the well-known risk-minimization approach. The correlation among multiple lines of business plays an important role in quantifying the uncertainty of loss reserves for insurance portfolios.
These modifications include discussions about time horizons, risk measures, financial returns, and valuation of insurance liabilities. This book was originally published as a special issue of the European Journal of Finance. Solvency of a business plan is defined by requiring as initial market value an additional amount over the one needed for solvability: this is the required solvency capital. Then we describe cost-of-capital margin calculations as they are used in practice. As an application, closed form analytical multiple integral formulas for pricing the European geometric basket option with a deflated multivariate exponential Wang variance-gamma asset pricing model are derived. The reach of the ideas is illustrated by discussing a wide range of applications and the models that have found wide usage.
These papers discuss insurance applications of asset pricing models, capital structure theory, and the economic theory of agency. The main purpose of this chapter is then to introduce a consistent multiperiod pricing framework. Let us assume for a moment that we can describe the risk by a random variable X as under a , describe the market conditions by a random variable Z. Topics covered are stochastic discounting with deflators, valuation portfolio in life and non-life insurance, probability distortions, asset and liability management, financial risks, insurance technical risks, and solvency. Risk management for financial institutions is one of the key topics the financial industry has to deal with. However, by now, they are among the standard interest-rate models see, e. Such a split is crucial because it explains which risks can be hedged at financial markets and which risks cannot be hedged and need to be absorbed by the insurance company.
Most stochastic claims reserving models assume independence between different accident years. Another objective was the establishment of confidence limits of reserves, at single treaty level as well as portfolio level. The concept of best-estimate, prescribed by regulators to value insurance liabilities for accounting and solvency purposes, has recently been discussed extensively in the industry and related academic literature. To fulfill this task we need to introduce the full balance sheet approach which is described in the present chapter. An extended Black-Scholes formula that takes into account the correlation structure of the market is also derived.
First, inspired by the idea of 'representation' of obligations by 'equivalent' assets, we define the supervisory provision or 'liability' attached to existing obligations. These models are supported by explicit applications to Swiss market financial data, and we analyze their strengths and weaknesses. Part 1 of the book presents 6 chapters related to financial applications; Part 2 presents 7 chapters on energy applications; and Part 3 presents 5 chapters devoted to specific theoretical and computational issues. The run off-pattern of long-term reinsurance treaties is described by means and standard deviations of logarithmic increments of premiums and loss ratios in a normal distribution. In general, a risk averse risk bearer of the insurance liabilities asks for an additional margin for settling the non-hedgeable insurance technical risks and for covering possible shortfalls in their development. Under certain assumptions, it is shown that these risk measures have properties similar to those of coherent risk measures.
I warmly recommend this book to graduate students and researchers in applied mathematics, financial mathematics, actuarial science, solvency and insurance. We find clear, different economic patterns in the local dynamics and regime specification of the yields depending on the maturity. In this chapter we introduce the valuation portfolio of Buchwalder—Bühlmann—Merz—Wüthrich. This study proposes a novel mathematical justification of a risk measure for stochastic processes as a map on a functional path space of future loss processes. The second is the economic equilibrium originally proposed by Borch. This is of course formalizing the way actuaries think about premiums.
Popular yield curve models include affine term structure models. Assuming that the financial market is complete, Pelsser and Stadje 2014 pro- posed a 'two-step' valuation which extends standard actuarial valuations into time-consistent and market-consistent valuations. Main features of this work are that we allow for hedging of the risk inherent in the life insurance liabili-ties by investing not only in the risky asset and the money market account, but also in an instrument representing the systematic mortality risk. The availability of the realizations of predicted claims permits us to perform a retrospective test, which suggests that extra prediction uncertainty is indispensable in modern risk management practices. A particular emphasis is given to the problem of finding optimal strategies for retained earnings which ensure a sustainable dividend policy. The motivation for this paper was the study of a multi-currency setting where it is natural to use simultaneously a domestic and a foreign asset as investment vehicles to inject the capital necessary to make an unacceptable position acceptable.