We assume that the claims liability process satisfies the distribution-free chain-ladder model assumptions. For claims reserving at time I we predict the total ultimate claim with the information available at time I and, similarly, at time 1 + I we predict the same total ultimate claim with the (updated) information available at time 1 + I . The claims development result at time 1 + I for accounting year ( ] 1 , + I I is then defined to be the difference between these two successive predictions for the total ultimate claim. In [6, 10] we have analyzed this claims development result and we have quantified its prediction uncertainty. Here, we simplify, modify and illustrate the results obtained in [6, 10]. We emphasize that these results have direct consequences for solvency considerations and were (under the new risk-adjusted solvency regulation) already implemented in industry.

/pdf/modelling-the-claims-development-result-for-solvency-4hefrkn5pj.pdf

Modelling The Claims Development Result For Solvency Purposes

New regulations and a stronger competition have increased the importance of stochastic asset–liability management (ALM) models for insurance companies in recent years. In this paper, we propose a discrete time ALM model for the simulation of simplified balance sheets of life insurance products. The model incorporates the most important life insurance product characteristics, the surrender of contracts, a reserve-dependent bonus declaration, a dynamic asset allocation and a two-factor stochastic capital market. All terms arising in the model can be calculated recursively which allows an easy implementation and efficient simulation. Furthermore, the model is designed to have a modular organization which permits straightforward modifications and extensions to handle specific requirements. In a sensitivity analysis for sample portfolios and parameters, we investigate the impact of the most important product and management parameters on the risk exposure of the insurance company and show that the model captures the main behaviour patterns of the balance sheet development of life insurance products.

/pdf/a-general-asset-liability-management-model-for-the-efficient-2iulmzmjyi.pdf

A general asset–liability management model for the efficient simulation of portfolios of life insurance policies

Over the last years the valuation of life insurance contracts using concepts from financial mathematics has become a popular research area for actuaries as well as financial economists. In particular, several methods have been proposed of how to model and price participating policies, which are characterized by an annual interest rate guarantee and some bonus distribution rules. However, despite the long terms of life insurance products, most valuation models allowing for sophisticated bonus distribution rules and the inclusion of frequently offered options assume a simple Black-Scholes setup and, in particular, deterministic or even constant interest rates. We present a framework in which participating life insurance contracts including predominant kinds of guarantees and options can be valuated and analyzed in a stochastic interest rate environment. In particular, the different option elements can be priced and analyzed separately. We use Monte Carlo and discretization methods to derive the respective values. The sensitivity of the contract and guarantee values with respect to multiple parameters is studied using the bonus distribution schemes as introduced in Bauer et al. (2006). Surprisingly, even though the value of the contract as a whole is only moderately affected by the stochasticity of the short rate of interest, the value of the different embedded options is altered considerably in comparison to the value under constant interest rates. Furthermore, using a simplified asset portfolio and empirical parameter estimations, we show that the proportion of stock within the insurer’s asset portfolio substantially affects the value of the contract.

/pdf/risk-neutral-valuation-of-participating-life-insurance-19acz4zkrc.pdf

Risk-neutral valuation of participating life insurance contracts in a stochastic interest rate environment

We present a novel stochastic model for claims reserving that allows us to combine claims payments and incurred losses information. The main idea is to combine two claims reserving models ( Hertig ’s ( 1985 ) model and Gogol ’s ( 1993 ) model ) leading to a log-normal paid–incurred chain (PIC) model. Using a Bayesian point of view for the parameter modelling we derive in this Bayesian PIC model the full predictive distribution of the outstanding loss liabilities. On the one hand, this allows for an analytical calculation of the claims reserves and the corresponding conditional mean square error of prediction. On the other hand, simulation algorithms provide any other statistics and risk measure on these claims reserves.

Paid-Incurred Chain Claims Reserving Method

In this chapter, we present various numerical experiments with different applications from finance. We study the performance of the different numerical quadrature methods from Chapter 3 and Chapter 4 and investigate the impact of the different approaches for dimension reduction and smoothing from Chapter 5. Parts of this chapter are taken from [58].

Validation and Applications

In this paper we present an approach to market based valuation of life insurance policies, in the spirit of the NUMAT proposed by Hans Buhlmann (2002) in an editorial in the ASTIN Bulletin. We have experienced the valuation method for more than one decade, both as a pricing procedure applied to policy portfolios of leading insurance companies, and by including the valuation principles into several actuarial teaching activities. Our interest is mainly focused here on participating policies that in Italy are characterized by contractually binding profit sharing rules. The problem of the fair valuation of the liabilities generated to the insurer by these contracts can be conveniently addressed using the methods of contingent claims pricing. These allow to price correctly the options embedded into the policies and to implement consistent plans of asset-liability management. The approach also provides a market based measurement of the value of business in force for outstanding policy portfolios and consistent assessments of the financial risk based capitals.

/pdf/market-based-tools-for-managing-the-life-insurance-company-2s2w8z4ouw.pdf

Market based tools for managing the life insurance company

In recent Solvency II considerations much effort has been put into the development of appropriate models for the study of the one-year loss reserving uncertainty in non-life insurance. In this article we derive formulas for the conditional mean square error of prediction of the one-year claims development result in the context of the Bayes chain ladder model studied in Gisler-Wuthrich. The key to these formulas is a recursive representation for the results obtained in Gisler-Wuthrich.

/pdf/recursive-credibility-formula-for-chain-ladder-factors-and-4ls5wv4qab.pdf

Recursive Credibility Formula for Chain Ladder Factors and the Claims Development Result

This technical report illustrates the basic principles for a fair valuation system in life insurance. The report is particularly concerned with the market consistent derivation of the Value of Business In Force (VBIF) for portfolios of profit-sharing policies, properly allowing for the cost of the embedded options and guarantees, according to the European Embedded Value Principles (EEVP) stated by the CFO Forum. Some relevant issues concerning the practical utilization of the system and the consistent interpretation of the results are illustrated by numerical examples. Particular attention has been paid to the harmonization with the results provided by more traditional valuation methods. The report is concluded by a description of some relevant details concerning the application of the valuation system to the life portfolios of the RAS Group.Results - The value of business in force (VBIF), the value of the minimum guaranteed return options (the put component of VBIF), the time value of the puts, the expected returns of the segregated funds and other quantities useful for controlling price and risk of the asset-liability portfolios are derived. Theoretical and practical issues are discussed concerning the theory of valuation, the market consistent pricing, the finance of insurance.The valuation procedure - The outstanding portfolios are analysed in the framework of the asset-liabilty valuation under uncertainty. The valuation of the financial components of future profits, as well as of the embedded options, is performed using a stochastic pricing model based on the no-arbitrage principle. The model is calibrated on market data, in order to capture the current interest rate levels, the interest rate volatilities, the stock price volatilities and correlations.In the valuation procedure closed form pricing expressions as well as Monte Carlo simulations are used. The accounting rules defining the segregated fund returns are allowed for. Financial uncertainty is analysed by modelling interest rate risk for each relevant currency, stock price risk, credit risk. Technical uncertainty is measured taking into account mortality/longevity risk, surrender risk, expenses inflation risk.Harmonization - Using the valuation system a logical connection can be created between the traditional approach - based on a single "best estimate" scenario - and the stochastic valuation model, specified under both the risk-neutral and the real world probabilities. Financial and technical risks, as well as the cost of the embedded options, are measured in terms of value (risk premiums and/or additional costs) and in terms of risk discount spread (discount rate margins).

http://mmenzietti.altervista.org/TAAV/Corso_AASNS_II.pdf

Embedded Value in Life Insurance

Market consistent valuation in life insurance. Measuring fair value and embedded options

Reserve Requirements and Capital Requirements in Non-Life Insurance. An analysis of the Italian MTPL insurance market by stochastic claims reserving models

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