An Introduction to Computational Risk Management of Equity-Linked Insurance: 1st Edition (Hardback) book cover

An Introduction to Computational Risk Management of Equity-Linked Insurance

1st Edition

By Runhuan Feng

CRC Press

382 pages | 30 B/W Illus.

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Hardback: 9781498742160
pub: 2018-06-12
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Description

The quantitative modeling of complex systems of interacting risks is a fairly recent development in the financial and insurance industries. Over the past decades, there has been tremendous innovation and development in the actuarial field. In addition to undertaking mortality and longevity risks in traditional life and annuity products, insurers face unprecedented financial risks since the introduction of equity-linking insurance in 1960s. As the industry moves into the new territory of managing many intertwined financial and insurance risks, non-traditional problems and challenges arise, presenting great opportunities for technology development.

Today's computational power and technology make it possible for the life insurance industry to develop highly sophisticated models, which were impossible just a decade ago. Nonetheless, as more industrial practices and regulations move towards dependence on stochastic models, the demand for computational power continues to grow. While the industry continues to rely heavily on hardware innovations, trying to make brute force methods faster and more palatable, we are approaching a crossroads about how to proceed. An Introduction to Computational Risk Management of Equity-Linked Insurance provides a resource for students and entry-level professionals to understand the fundamentals of industrial modeling practice, but also to give a glimpse of software methodologies for modeling and computational efficiency.

Features

  • Provides a comprehensive and self-contained introduction to quantitative risk management of equity-linked insurance with exercises and programming samples
  • Includes a collection of mathematical formulations of risk management problems presenting opportunities and challenges to applied mathematicians
  • Summarizes state-of-arts computational techniques for risk management professionals
  • Bridges the gap between the latest developments in finance and actuarial literature and the practice of risk management for investment-combined life insurance
  • Gives a comprehensive review of both Monte Carlo simulation methods and non-simulation numerical methods

Runhuan Feng is an Associate Professor of Mathematics and the Director of Actuarial Science at the University of Illinois at Urbana-Champaign. He is a Fellow of the Society of Actuaries and a Chartered Enterprise Risk Analyst. He is a Helen Corley Petit Professorial Scholar and the State Farm Companies Foundation Scholar in Actuarial Science. Runhuan received a Ph.D. degree in Actuarial Science from the University of Waterloo, Canada. Prior to joining Illinois, he held a tenure-track position at the University of Wisconsin-Milwaukee, where he was named a Research Fellow.

Runhuan received numerous grants and research contracts from the Actuarial Foundation and the Society of Actuaries in the past. He has published a series of papers on top-tier actuarial and applied probability journals on stochastic analytic approaches in risk theory and quantitative risk management of equity-linked insurance. Over the recent years, he has dedicated his efforts to developing computational methods for managing market innovations in areas of investment combined insurance and retirement planning.

Reviews

"I am sitting in Donza, the best coffeeshop in Deinze, reading Runhuan Feng's new book. WHAT A MARVELOUS BOOK!!! Full of very interesting facts, very well written at the right level. There should be more actuarial books like that. Congratulations Runhuan Feng for the highly valuable text." ~Jan Dhaene, KU Leuven

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

It^o'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

About the Author

Author

Runhuan Feng

Champaign, Illinois, United States of America

Learn more about Runhuan Feng >>

Runhuan Feng is an Associate Professor of Mathematics and the Director of Actuarial Science at the University of Illinois at Urbana-Champaign. He is a Fellow of the Society of Actuaries and a Chartered Enterprise Risk Analyst. He is a Helen Corley Petit Professorial Scholar and the State Farm Companies Foundation Scholar in Actuarial Science. Runhuan received a Ph.D. degree in Actuarial Science from the University of Waterloo, Canada. Prior to joining Illinois, he held a tenure-track position at the University of Wisconsin-Milwaukee, where he was named a Research Fellow.

Runhuan received numerous grants and research contracts from the Actuarial Foundation and the Society of Actuaries in the past. He has published a series of papers on top-tier actuarial and applied probability journals on stochastic analytic approaches in risk theory and quantitative risk management of equity-linked insurance. Over the recent years, he has dedicated his efforts to developing computational methods for managing market innovations in areas of investment combined insurance and retirement planning.

About the Series

Chapman and Hall/CRC Financial Mathematics Series

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
BUS027000
BUSINESS & ECONOMICS / Finance
MAT000000
MATHEMATICS / General
MAT029000
MATHEMATICS / Probability & Statistics / General