05610nam 2200709 a 450 991083012130332120230802012943.01-118-56203-81-299-31580-11-118-56593-2(CKB)2560000000100658(EBL)1143593(OCoLC)830161735(SSID)ssj0000834203(PQKBManifestationID)11966445(PQKBTitleCode)TC0000834203(PQKBWorkID)10936514(PQKB)11334741(OCoLC)841171575(MiAaPQ)EBC1143593(EXLCZ)99256000000010065820111208d2012 uy 0engur|n|---|||||txtccrStochastic methods for pension funds[electronic resource] /Pierre Devolder, Jacques Janssen, Raimondo MancaLondon ISTE Ltd. ;Hoboken, N.J. Wiley20121 online resource (476 p.)Applied stochastic methods seriesDescription based upon print version of record.1-84821-204-6 Includes bibliographical references and index.Cover; 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 Funding2.1. 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 control3.2.1. 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 problem3.5.2. 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 preliminaries4.4.2. 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 cases5.5.3. Yield curve associated with an instantaneous interest rateQuantitative 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 cApplied stochastic methods series.Pension trustsManagementPension trustsMathematicsFinancial risk managementMathematical modelsStochastic modelsPension trustsManagement.Pension trustsMathematics.Financial risk managementMathematical models.Stochastic models.332.67/2540151923332.672540151923Devolder Pierre614083Janssen Jacques1939-102056Manca Raimondo327298MiAaPQMiAaPQMiAaPQBOOK9910830121303321Stochastic methods for pension funds3979354UNINA