An Introduction to Computational Risk Management of Equity-Linked Insurance.
"The book will be devoted to quantitative models and computational techniques for risk management of equity-linked insurance. Although there have been research papers on the valuation of a great variety of investment guarantee products, they were primarily based on financial option pricing theo...
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| Format: | eBook |
| Language: | English |
| Published: |
Boca Raton, FL :
CRC Press,
2017.
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| Edition: | First edition. |
| Series: | Chapman and Hall/CRC Financial Mathematics Series
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Modeling of Equity-linked Insurance
- Fundamental principles of traditional insurance
- Time value of money
- Law of large numbers
- Equivalence premium principle
- Central limit theorem
- Portfolio percentile premium principle
- Variable annuities
- Mechanics of deferred variable annuity
- Resets, roll-ups and ratchets
- Guaranteed minimum maturity benefit
- Guaranteed minimum accumulation benefit
- Guaranteed minimum death benefit
- Guaranteed minimum withdrawal benefit
- Guaranteed lifetime withdrawal benefit
- Mechanics of immediate variable annuity benefit
- Modeling of immediate variable annuity
- Single premium vs flexible premium annuities
- Fundamental principles of equity-linked insurance
- Equity-indexed annuities
- Point-to-point designs
- Cliquet designs
- High water mark designs
- Bibliographic notes
- Exercises
- Elementary Stochastic Calculus
- Probability space
- Random variable
- Expectation
- Discrete random variable
- Continuous random variable
- Stochastic process and sample path
- Conditional expectation
- Martingale versus Markov processes
- Scaled random walks
- Brownian motion
- Stochastic integral
- Itô's formula
- Stochastic differential equation
- Applications to equity-linked insurance
- Stochastic equity returns
- Guaranteed withdrawal benefits
- Laplace transform of ruin time
- Present value of total fees up to ruin
- Stochastic interest rates
- Vasicek model
- Cox-Ingersoll-Ross (CIR) model
- Exercises
- Monte Carlo Simulations of Investment Guarantees
- Simulating continuous random variables
- Inverse transformation method
- Rejection method
- Simulating discrete random variables
- Simulating continuous-time stochastic processes
- Exact joint distribution
- Brownian motion
- Geometric Brownian motion
- Vasicek process
- Euler discretization
- Euler method
- Milstein method
- Economic scenario generator
- Exercises
- Pricing and Valuation
- No-arbitrage pricing
- Discrete time pricing: binomial tree
- Pricing by replicating portfolio
- Representation by conditional expectation
- Dynamics of self-financing portfolio
- Continuous time pricing: Black-Scholes model
- Pricing by replicating portfolio
- Representation by conditional expectation
- Risk-neutral pricing
- Path-independent derivatives
- Path-dependent derivatives
- No arbitrage costs of investment guarantees
- Guaranteed minimum maturity benefit
- Guaranteed minimum accumulation benefit
- Guaranteed minimum death benefit
- Guaranteed minimum withdrawal benefit
- Policyholder's perspective
- Insurer's perspective
- Equivalence of pricing
- Guaranteed lifetime withdrawal benefit
- Policyholder's perspective
- Insurer's perspective
- Actuarial pricing
- Mechanics of profit testing
- Actuarial pricing vs no-arbitrage pricing
- Exercises
- Risk Management
- Reserving and Capital Requirement
- Reserve and capital
- Risk measures
- Value-at-Risk
- Conditional tail expectation
- Coherent risk measure
- Tail-value-at-risk
- Distortion risk measure
- Comonotonicity
- Statistical inference of risk measures
- Risk aggregation
- Variance-covariance approach
- Model uncertainty approach
- Scenario aggregation approach
- Liability run-o_ approach
- Finite horizon mark-to-market approach
- Risk diversification
- Convex ordering
- Thickness of tail
- Conditional expectation
- Individual model vs aggregate model
- Law of large numbers for equity-linked insurance
- Identical and fixed initial payments
- Identically distributed initial payments
- Risk engineering of variable annuity guaranteed benefits
- Capital allocation
- Pro-rata principle
- Euler principle
- Stochastic reserving by example
- Exercises
- Risk Management
- Dynamic Hedging
- Discrete time hedging: binomial tree
- Replicating portfolio
- Hedging portfolio
- Continuous time hedging: Black-Scholes model
- Greek letters hedging
- Advanced Computational Methods
- Differential equation methods
- Reduction of dimension
- Laplace transform method
- General methodology
- Application
- Finite difference method
- General methodology
- Application
- Application to guaranteed minimum withdrawal benefit
- Value-at-risk of individual net liability
- Conditional tail expectation of individual net
- liability
- Numerical example
- Comonotonic approximation
- Tail value-at-risk of conditional expectation
- Comonotonic bounds for sums of random variables
- Guaranteed minimum maturity benefit
- Application to guaranteed minimum benefit
- Guaranteed minimum death benefit
- Nested stochastic modeling
- Preprocessed inner loops
- Least-squares Monte Carlo
- Application to guaranteed lifetime withdrawal benefit
- Overview of nested structure
- Outer loop: surplus calculation
- Inner loop: risk-neutral valuation
- Computational techniques
- Exercises.