《Market-Consistent Actuarial Valuation》
Mario Valentin Wüthrich• Hans Bühlmann • Hansjörg Furrer
EAA Lecture NotesEditorsH. Bühlmann A. PelsserW. Schachermayer H. Waters D. Filipovic, ChairEAA Lecture Notes is a series supported by the European ActuarialAcademy (EAA GmbH), founded on the29 August,2005 in Cologne(Germany) by the Actuarial Associations of Austria, Germany,the Netherlands and Switzerland. EAA offers actuarial educationincluding examination, permanent education for certified actuaries andconsulting on actuarial education.
Contents1 Introduction ............................................... 11.1 Three pillar approach .................................... 11.2 Solvency ............................................... 21.3 Fromthe past to the future............................... 41.4 Full balance sheet approach . . ............................. 41.5 Recent financial failures and difficulties ..................... 62 Stochastic discounting ..................................... 72.1 Basicdiscrete time model ................................ 72.2 Market-consistent valuation in the basic discrete time model . . 92.2.1 Task of modelization . .............................. 122.2.2 Understanding deflators . . .......................... 122.2.3 Toy example for deflators . .......................... 142.3 Valuation at time t> 0 .................................. 162.4 The meaning ofbasic reserves............................. 182.5 Equivalent martingale measures . . ......................... 202.6 Technical and financial variables........................... 242.7 Conclusions on Chapter 2 ................................ 263 Valuation portfolio in life insurance ........................ 293.1 Deterministic lifeinsurance model ......................... 293.2 Valuation portfolio for deterministic life model . . . . .......... 303.3 General valuation procedure for deterministic technical risks . . 323.4 Self-financing property of the VaPo (deterministic technicalrisk) ................................................... 333.5 VaPo protected against technical risks . ..................... 343.6 Backto the basicmodel.................................. 393.7 Conclusion on Chapter 3 ................................. 403.8 Examples............................................... 41VIII Contents4 Financial risks ............................................. 474.1 Asset liability management . . . ............................ 474.2 Procedure to control financial risks ........................ 494.3 Financial modeling ...................................... 514.3.1 Stochastic discounting . ............................ 514.3.2 Modeling Margrabe options......................... 524.3.3 Conclusions . . . . . . . ................................ 534.4 Pricing Margrabeoptions................................. 534.4.1 Pricing using Esscher transforms .................... 544.4.2 Application of the Esscher transform to themulti-dimensional Wiener process ................... 574.4.3 Hedging Margrabe options . . ........................ 594.4.4 Risk bearing capital . . . ............................ 615 Valuation portfolio in non-life insurance ................... 635.1 Introduction ............................................ 635.2 Construction ofthe VaPo................................. 665.3 VaPo protected against technical risks, pragmatic approach . . . 685.4 VaPo protected against technical risks, theoreticalconsiderations........................................... 705.5 Loss development triangles ............................... 735.5.1 Definitions ....................................... 735.5.2 Chain-ladder method . . ............................ 765.5.3 Estimation of the technical risks in the chain-laddermodel, single accidentyear ......................... 835.5.4 Aggregation of parameter risks across differentaccident years..................................... 935.6 Unallocated loss adjustment expenses . . .................... 975.6.1 Motivation ....................................... 975.6.2 Pure claims payments . . ............................ 985.6.3 ULAE charges . . . . ................................ 995.6.4 New York-method . ................................1005.6.5 Example . ........................................1045.7 Conclusion on the non-life VaPo...........................1046 Selected Topics ............................................1076.1 Sources of losses and profits, profit sharing..................1076.2 Remarks on the self-financing property . ....................1096.3 Legal quote in lifeinsurance ..............................111References.....................................................115Index .............................. ............................119