LEADER 05610nam 2200709 a 450 001 9910830121303321 005 20230802012943.0 010 $a1-118-56203-8 010 $a1-299-31580-1 010 $a1-118-56593-2 035 $a(CKB)2560000000100658 035 $a(EBL)1143593 035 $a(OCoLC)830161735 035 $a(SSID)ssj0000834203 035 $a(PQKBManifestationID)11966445 035 $a(PQKBTitleCode)TC0000834203 035 $a(PQKBWorkID)10936514 035 $a(PQKB)11334741 035 $a(OCoLC)841171575 035 $a(MiAaPQ)EBC1143593 035 $a(EXLCZ)992560000000100658 100 $a20111208d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aStochastic methods for pension funds$b[electronic resource] /$fPierre Devolder, Jacques Janssen, Raimondo Manca 210 $aLondon $cISTE Ltd. ;$aHoboken, N.J. $cWiley$d2012 215 $a1 online resource (476 p.) 225 1 $aApplied stochastic methods series 300 $aDescription based upon print version of record. 311 $a1-84821-204-6 320 $aIncludes bibliographical references and index. 327 $aCover; Stochastic Methods for Pension Funds; Title Page; Copyright Page; Table of Contents; Preface; Chapter 1. Introduction: Pensions in Perspective; 1.1. Pension issues; 1.1.1. The challenge; 1.1.2. Some figures; 1.2. Pension scheme; 1.2.1. Definition; 1.2.2. The four dimensions of a pension scheme; 1.3. Pension and risks; 1.3.1. Demographic risks; 1.3.2. Financial risks; 1.3.3. Impact of the risks on various kinds of pension schemes; 1.3.4. The time horizon of a pension scheme; 1.4. The multi-pillar philosophy; Chapter 2. Classical Actuarial Theory of Pension Funding 327 $a2.1. General equilibrium equation of a pension scheme2.1.1. Principles; 2.1.2. The retrospective reserve; 2.1.3. The prospective reserve; 2.1.4. Equilibrated pension funding; 2.1.5. Decomposition of the reserve; 2.1.6. Classification of the methods; 2.2. General principles of funding mechanisms for DB Schemes; 2.3. Particular funding methods; 2.3.1. Unit credit cost methods; 2.3.2. Level premium methods; 2.3.3. Aggregate cost methods; Chapter 3. Deterministic and Stochastic Optimal Control; 3.1. Introduction; 3.2. Deterministic optimal control 327 $a3.2.1. Formulation of the optimal control problem3.3. Necessary conditions for optimality; 3.3.1. Bellman function; 3.3.2. Bellman optimality equation; 3.3.3. Hamilton-Jacobi equation; 3.3.4. The synthesis function; 3.3.5. Other types of optimal controls; 3.3.6. Example: the classical quadratic/linear control problem; 3.4. The maximum principle; 3.4.1. The maximum principle from the dynamic programming approach; 3.5. Extension to the one-dimensional stochastic optimal control; 3.5.1. Formulation of the one-dimensional stochastic optimal control problem 327 $a3.5.2. Necessary conditions for one-dimensional stochastic optimality3.5.3. Extension to the multi-dimensional stochastic optimal control; 3.5.4. Dynamic programming principle; 3.5.5. The Hamilton-Jacobi-Bellman equation; 3.6. Examples; 3.6.1. Merton portfolio allocation problem; Chapter 4. Defined Contribution and Defined Benefit Pension Plans; 4.1. Introduction; 4.2. The defined benefit method; 4.3. The defined contribution method; 4.3.1. The model; 4.3.2. The capitalization system; 4.4. The notional defined contribution (NDC) method; 4.4.1. Historical preliminaries 327 $a4.4.2. The Dini reform transformation coefficients4.4.3. Theoretical preliminaries; 4.4.4. The construction of a unitary pension present value; 4.4.5. Numerical example and results comparison; 4.5. Conclusions; Chapter 5. Fair and Market Values and Interest Rate Stochastic Models; 5.1. Fair value; 5.2. Market value of financial flows; 5.3. Yield curve; 5.4. Yield to maturity for a financial investment and for a bond; 5.5. Dynamic deterministic continuous time model for an instantaneous interest rate; 5.5.1. Instantaneous interest rate; 5.5.2. Particular cases 327 $a5.5.3. Yield curve associated with an instantaneous interest rate 330 $aQuantitative finance has become these last years a extraordinary field of research and interest as well from an academic point of view as for practical applications. At the same time, pension issue is clearly a major economical and financial topic for the next decades in the context of the well-known longevity risk. Surprisingly few books are devoted to application of modern stochastic calculus to pension analysis. The aim of this book is to fill this gap and to show how recent methods of stochastic finance can be useful for to the risk management of pension funds. Methods of optimal c 410 0$aApplied stochastic methods series. 606 $aPension trusts$xManagement 606 $aPension trusts$xMathematics 606 $aFinancial risk management$xMathematical models 606 $aStochastic models 615 0$aPension trusts$xManagement. 615 0$aPension trusts$xMathematics. 615 0$aFinancial risk management$xMathematical models. 615 0$aStochastic models. 676 $a332.67/2540151923 676 $a332.672540151923 700 $aDevolder$b Pierre$0614083 701 $aJanssen$b Jacques$f1939-$0102056 701 $aManca$b Raimondo$0327298 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830121303321 996 $aStochastic methods for pension funds$93979354 997 $aUNINA